Integration Lesson

1

Multiple Choice

∫(3x⁴+2)⁴(12x³)dx

1

½(3x⁴+2)⁴+C

2

(3x⁴+2)⁴+C

3

⅕(3x⁴+2)⁵+C

4

⅓(3x⁴+2)⁶+C

2

Multiple Choice

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

1

$\frac{ax^{n+1}}{n+1}$

2

$\frac{ax^{n-1}}{n-1}+\ c$

3

$\frac{ax^{n+1}}{n}+\ c$

4

$\frac{ax^{n+1}}{n+1}+\ c$

3

Multiple Choice

∫ 6 x (x² +1 )² dx

1

( x² + 1)³ + C

2

3 ( x² + 1)³ + C

3

( x² + 1)¹ + C

4

6 ( x² + 1)³ + C

4

Multiple Choice

$\int5x^4dx$

1

$x^5$

2

$\frac{5}{4}x^5+C$

3

$x^5+C$

4

$20x^3$ + C

5

Multiple Choice

1

⅝

2

-⅝

3

⅜

4

45/16

6

Multiple Choice

Which of the following is TRUE ?

1

$\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +c$

2

$\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ c$

3

$\int_{ }^{ }\ \frac{1}{x}\ \ dx\ =\ \ln\ \left|x\ \right|\ +c$

4

$\int_{ }^{ }\ x\ \ dx\ =\ 1\ +\ c$

7

Multiple Choice

Solve $\int\left(8x^3-2x\right)dx$

1

$2x^4-x^2+C$

2

$4x^{4\ }-2x+C$

3

$x^4-2x+C$

4

$12x^4-x^2+C$

8

Multiple Choice

$\int1\cdot\ dx=$

1

$0$

2

$1$

3

$2$

4

$x+C$

9

Multiple Choice

∫ 2 x (x²- 3)^(1/2) dx

1

(x²- 3)^(3/2)+C

2

(3/2)(x²- 3)^(3/2)+C

3

(2/3)(x²- 3)^(3/2)+C

4

(2/3)(x²- 3)^(-1/2)+C

10

Multiple Choice

\int_{ }^{ }x^n\ dx=

1

$n\cdot x^{n-1}$

2

$n\cdot x^{n+1}$

3

$\frac{x^{n+1}}{n+1}$

4

$\frac{x^{n+1}}{n+1}+C$ where $n\ne-1$

11

Multiple Choice

Solve $\int6x\left(x+2\right)dx$

1

$6x^2+12x+C$

2

$x^{2\ }-2x+C$

3

$3x^2+6x+C$

4

$2x^3+6x^2+C$

12

Multiple Choice

\int\frac{1}{x^n}dx=_{ }

_____________ for

n\ne1

1

$\frac{n}{x^{n-1}}+C$

2

$\frac{-n}{x^{n-1}}+C$

3

$\frac{-n}{x^{n+1}}+C$

4

$\frac{n}{x^{n+1}}+C$

13

Multiple Choice

$\int_{ }^{ }x^3\ -\pi\ dx\ \ =$

1

$3x^2\ +\ c$

2

$\frac{x^4}{4}\ +\ c$

3

$\frac{x^4}{4}\ -\ \pi x$

4

$\frac{x^4}{4}\ -\ \pi x\ +\ c$

14

Multiple Choice

\int\frac{1}{x}dx=

_____________

1

$\frac{-1}{x^2}+C$

2

$\frac{1}{x^2}+C$

3

$\log\left|x\right|+C$

4

None of these

15

Multiple Choice

Solve $\int\left(e^{7x}-\frac{5}{2x^3}\right)dx$

1

$\frac{e^{7x}}{7}-\frac{5}{8x^4}+C$

2

$\frac{e^{7x}}{7}+\frac{5}{4x^2}+C$

3

$7e^{7x}-\frac{5}{8x^4}+C$

4

$\frac{e^{7x}}{8x}+\frac{5}{4x^2}+C$

16

Multiple Choice

\int\frac{1}{\sqrt{x}}dx=

\

1

$\sqrt{x}+C$

2

$2\sqrt{x}+C$

3

$x+C$

4

$2x+C$

17

Multiple Choice

∫3x²(x³-9)^2/3 dx

1

(3x²)^4/3

2

(2/3)(x³-9)^5/3

3

3(x³-9)^-1/3

4

-3(x³-9)^-1/3

18

Multiple Choice

\int a^x\ dx=

___________

(where

a>0;\ a\ne1

)

1

$a^x\cdot\log_{ }a+C$

2

$\frac{a^x}{\log_{ }a}+C$

3

$\frac{\log_{ }a}{a^x}+C$

4

$a^x+C$

19

Multiple Choice

$\int\left(5\sqrt{x^3}-16e^{-4x}+\frac{1}{x}\right)dx$

1

$2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$

2

$5x^{\frac{1}{3}}+4e^{-4x}+\ln\left|x\right|+C$

3

$2x^{\frac{5}{2}}-4e^{-4x}+\ln\left|x\right|+C$

4

Nothing is correct

20

Multiple Choice

\int e^x\ dx=

___________

1

$e^x+C$

2

$x+C$

3

$C$

4

None of these

21

Multiple Choice

What is $\int_{ }^{ }\ \frac{5}{x^6}\ dx$ ?

1

$5x^{-6}\ +\ c$

2

$5x^{-5}\ +\ c$

3

$-\frac{5}{4x^4}\ +\ c$

4

$-\frac{1}{x^5}\ +\ c$

22

Multiple Choice

\int\sin x\ dx=

___________

1

$\cos x+C$

2

$-\cos x+C$

3

$e^{\sin x}+C$

4

None of these

23

Multiple Choice

Solve $\int_{ }^{ }2\sin\left(\frac{x}{5}\right)dx$

1

$\cos\left(\frac{x}{5}\right)+C$

2

$-\frac{2}{5}\cos\left(\frac{x}{5}\right)+C$

3

$-10\cos\left(\frac{x}{5}\right)+C$

4

$-2\cos\left(5x\right)+C$

24

Multiple Choice

\int\cos x\ dx=

___________

1

$\sin x+C$

2

$-\sin x+C$

3

$e^{\cos x}+C$

4

None of these

25

Multiple Choice

$\int\left(x^2-2x\right)dx$

1

$\frac{1}{3}x^3-x^2+C$

2

$x^{2\ }-2x+C$

3

$2x-2$

4

$\frac{1}{3}x^3-x^2$

26

Multiple Choice

\int\tan x\ dx=

___________

1

$\sec^2x+C$

2

$\ell n\left|\sec x\right|+C$

3

$\ell n\left|\cos x\right|+C$

4

$\sec x\cdot\tan x+C$

27

Multiple Choice

Solve $\int12x^3\left(3x^4+2\right)^4\ dx$

1

$\frac{1}{2}\left(3x^4+2\right)^4+C$

2

$5\left(3x^4+2\right)^5+C$

3

$\frac{1}{5}\left(3x^4+2\right)^5+C$

4

$\frac{1}{3}\left(3x^4+2\right)^6+C$

28

Multiple Choice

\int\cot x\ dx=

___________

1

$-\operatorname{cosec}^2x+C$

2

$\ell n\left|\operatorname{cosec}x\right|+C$

3

$\ell n\left|\sin x\right|+C$

4

$-\operatorname{cosec}x\cdot\cot x+C$

29

Multiple Choice

Integrate $\int_{ }^{ }\cos\ \left(5x\right)\ dx$ with respect to x.

1

$\sin\ \left(5x\right)\ +\ c$

2

$-\frac{1}{5}\sin\ \left(5x\right)\ +\ c$

3

$\frac{1}{5}\ \sin\ \left(5x\right)\ +\ c$

4

$\frac{\cos\ \left(5x\right)}{5}\ +\ c$

30

Multiple Choice

\int\operatorname{cosec}x\ dx=

___________

1

$-\operatorname{cosec}x\cdot\cot x+C$

2

$\ell n\left|\operatorname{cosec}x\right|+C$

3

$-\cot^2x+C$

4

$\ell n\left|\operatorname{cosec}x-\cot x\right|+C$

31

Multiple Choice

Solve $\int_{ }^{ }e^x\cos\left(e^x+6\right)\ dx$

1

$\frac{1}{6}\cos\left(e^x+6\right)+C$

2

$\sin\left(e^x+6\right)+C$

3

$-\sin\left(e^x+6\right)+C$

4

$\frac{1}{6}e^x\sin\left(e^x+6\right)+C$

32

Multiple Choice

\int\sec x\ dx=

___________

1

$\sec x\cdot\tan x+C$

2

$\ell n\left|\sec x\right|+C$

3

$\ell n\left|\sec x+\tan x\right|+C$

4

$\tan^2x+C$

33

Multiple Choice

∫e^xsin(e^x+6) dx

1

-cos(e^x+6) + C

2

cos(e^x+6) +C

3

sin(e^x+6)+C

4

e^2x/2

34

Multiple Choice

\int\sec^2x\ dx=

___________

1

$\tan x+C$

2

$2\sec^2x\ \tan x+C$

3

$\ell n\left|\tan x\right|+C$

4

$\operatorname{cosec}^2x+C$

35

Multiple Choice

Solve $\int\ \frac{2x}{5-3x^2}dx^{ }$

1

$-\frac{1}{3}\ln\left|5-3x^2\right|+C$

2

$\frac{1}{6}\ln\left|5-3x^2\right|+C$

3

$-\frac{5}{3}\ln\left|5-3x^2\right|+C$

4

$-\frac{1}{2x}\ln\left|5-3x^2\right|+C$

36

Multiple Choice

\int\operatorname{cosec}^2x\ dx=

___________

1

$-2\ \operatorname{cosec}^2x\ \cot x+C$

2

$\cot x+C$

3

$-\cot x+C$

4

$\sec^2x+C$

37

Multiple Choice

Which is the integral of $\int_{ }^{ }\ \left(5-3x\right)^3\ dx$ ?

1

$3\left(5-3x\right)^2\ +c$

2

$\frac{\left(5-3x\right)^4}{4}+\ c$

3

$\frac{\left(5-3x\right)^4}{12}+\ c$

4

$-\frac{\left(5-3x\right)^4}{12}+\ c$

38

Multiple Choice

\int\sec x\ \tan x\ dx=

___________

1

$\ell n\left|\sec x\right|+C$

2

$\sec x+C$

3

$-\sec x+C$

4

$\sec x\ \tan x+C$

39

Multiple Choice

What does C represent in an antiderivative?

1

A variable

2

A constant

3

None of these

4

Unknown

40

Multiple Choice

\int\operatorname{cosec}x\ \cot x\ dx=

___________

1

$\operatorname{cosec}x+C$

2

$-\operatorname{cosec}x+C$

3

$-\operatorname{cosec}x\ \cot x+C$

4

$-\cot^2x+C$

41

Multiple Choice

∫ 2x cos(x²) dx

1

sin(x²) + C

2

2 sin ( 2x ) + C

3

(1/2) sin(x²) + C

4

4 cos(2x ) + C

42

Multiple Choice

What is an antiderivative?

1

The opposite of a derivative

2

The same as a derivative

3

A second derivative

4

It always represents velocity.

43

Multiple Choice

Which of the following is NOT one of techniques of Integration?

1

Substitution

2

By Part

3

Quotient Rule

4

Partial Fraction

44

Multiple Choice

Solve $\int_{-1}^0\ 10x\left(1+x\right)^8\ dx$

1

$-\frac{1}{9}$

2

$\frac{1}{9}$

3

$-\frac{1}{90}$

4

$0$

45

Multiple Choice

$\frac{d}{dx}\left[e^{2x}\ +\ 3x^2+5\right]$

1

$e^{2x}+\ 6x^2$

2

$2e^{2x}\ +6x\$

3

$2e^x+6x\$

4

none of these

46

Multiple Choice

Solve $\int_{ }\frac{\left(\ln3x\right)^4}{x}dx$

1

$\frac{\ln\left(3x\right)^5}{5}+C$

2

$\frac{\left(\ln3x\right)^5}{5}+C$

3

$\ln3x+C$

4

$\frac{\left(\ln3x\right)^5}{15}+C$

47

Multiple Choice

Using integration by part, if given that u = (x + 1) then find v for $\int\left(x\ +1\right)\ e^{2x}\ dx$

1

$\frac{x^2}{2}+x$

2

$e^{2x}$

3

$2e^{2x}$

4

$\frac{e^{2x}}{2}$

48

Multiple Choice

Solve $\int_{ }\left(2-3\tan x\right)^4\sec^2x\ dx$

1

$\frac{1}{5}\left(2-3\tan x\ \right)^5+C$

2

$-\frac{1}{3}\left(2-3\tan x\ \right)^5+C$

3

$-\frac{1}{5}\left(2-3\tan x\ \right)^5+C$

4

$-\frac{1}{15}\left(2-3\tan x\ \right)^5+C$

49

Multiple Choice

$\int6x\left(x+2\right)dx$

1

$6x^2+12x+C$

2

$x^{2\ }-2x+C$

3

$3x^2+6x+C$

4

$2x^3+6x^2+C$

50

Multiple Choice

Which of the following is TRUE ?

1

$\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +C$

2

$\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ C$

3

$\int_{ }^{ }\ 2x\ \ dx\ =\ x^2\ +C$

4

$\int_{ }^{ }\ \frac{1}{x^2}\ \ dx\ =\ \ln\left|x^2\right|+C$

51

Multiple Choice

Integrate the partial fraction with respect to x
$\int_{ }^{ }\ \frac{1}{\left(x\right)}\ +\ \frac{4}{\left(2x\ -1\ \right)}\ dx$

1

$\ln\ \left|x\right|\ +\ 8\ \ln\left|2x-1\right|+c$

2

$\ln\ \left|x\right|\ +\ 4\ \ln\ \left|x-1\right|+c$

3

$\ln\ \left|x\right|\ +\ 4\ \ln\left|2x-1\right|+c$

4

$\ln\ \left|x\right|\ +\ 2\ \ln\left|2x-1\right|+c$

52

Multiple Choice

Solve $\int\left(x^5\ -\pi\ \right)dx\ \$

1

$5x^6\ +C$

2

$\frac{x^6}{6}\ +C$

3

$\frac{x^6}{6}\ -\ \pi x+C$

4

$\frac{x^6}{6}\ -\ \pi\ +\ C$

53

Multiple Choice

$\int_{ }^{ }e^{5x}dx\ =$

1

$e^{5x}+c$

2

$5e^{5x}+c$

3

$\frac{1}{5}e^{5x}+c$

4

none of these

54

Multiple Choice

Evaluate $\int_1^2\ \ 3x^2\ \ dx$

1

$7$

2

$8$

3

$12$

4

$x^3$

55

Multiple Choice

Which of the following is the indefinite integral of $\frac{x^3}{2}+7$ ?

1

$\frac{3x^2}{2}$

2

$\frac{3x^2}{2}+7x+c$

3

$\frac{x^4}{8}+7x+c$

4

$\frac{x^4}{8}+c$

56

Multiple Choice

Evaluate the integral $\int_0^2\ \frac{x^3\ +\ x^2}{x^2}\ dx$

1

$2$

2

$4$

3

$6$

4

$8$

57

Multiple Choice

∫(cos x + 3x²)dx =

1

-sin x + x³ + c

2

sinx + x³ + c

3

-sin x + 6x

4

🌞

58

Multiple Choice

$\int\left(6\sqrt{x}-1\right)dx$

1

$6x^{\frac{3}{2}}+x+C$

2

$4x^{\frac{3}{2}}-x+C$

3

$3x^{-\frac{1}{2}}-x+C$

4

I didn't look at my notes to see how to do this one.

59

Multiple Choice

$\int\ \frac{2}{x+3}dx^{ }=$

1

2ln|x+3| + c

2

2ln(x + 3) + c

3

$\frac{1}{2}\ln\left|x\ +\ 3\right|\ +\ c$

4

none of these

60

Multiple Choice

1

ln(2x²+6) + C

2

ln(2x²+6)(4x) + C

3

1/(2x²+6) + C

4

1/(2x²+6)²+ C

61

Multiple Choice

∫cos(4x+5)dx

1

-¼sin(4x + 5) + C

2

4sin(4x + 5) + C

3

¼sin(4x + 5) + C

4

4cos(4x + 5) + C

62

Multiple Choice

$\int\left(\frac{1}{x^2}+\frac{6}{x^3}\right)dx$

1

$-x^{-1}-3x^{-2}+C$

2

$\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C$

3

$-x^{-1}-3x^{-2}$

4

$-x-3x^2+C$

63

Multiple Choice

$\int\left(\frac{4}{x}-e_{ }^x\right)dx$

1

$4\ln\left(x\right)-e^x$

2

$4\ln\left(x\right)+e^x+C$

3

$4\ln\left(x\right)-e^x+C$

4

$\frac{4}{x^2}-4e^x+C$

64

Multiple Choice

∫ 6 x (x² +1 )² dx

1

( x² + 1)³ + C

2

3 ( x² + 1)³ + C

3

( x² + 1)¹ + C

4

6 ( x² + 1)³ + C

65

Multiple Choice

Which of the following is TRUE ?

1

$\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +c$

2

$\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ c$

3

$\int_{ }^{ }\ \frac{1}{x}\ \ dx\ =\ \ln\ \left|x\ \right|\ +c$

4

$\int_{ }^{ }\ x\ \ dx\ =\ 1\ +\ c$

66

Multiple Choice

$\int\left(5x^2-7x+6\right)dx$

1

$\frac{5}{3}x-\frac{7}{2}x+6x+C$

2

$x+x+x+x+x+C$

3

$x^3-3x^2+6x+C$

4

$\frac{5}{3}x^3-\frac{7}{2}x^2+6x+C$

67

Multiple Choice

$\int_{ }^{ }x^3\ -\pi\ dx\ \ =$

1

$3x^2\ +\ c$

2

$\frac{x^4}{4}\ +\ c$

3

$\frac{x^4}{4}\ -\ \pi x$

4

$\frac{x^4}{4}\ -\ \pi x\ +\ c$

68

Multiple Choice

What should be used for u in the integral?

1

no u needed

2

4t²

3

t³

4

1/4t²

69

Multiple Choice

What is $\int_{ }^{ }\ \frac{5}{x^6}\ dx$ ?

1

$5x^{-6}\ +\ c$

2

$5x^{-5}\ +\ c$

3

$-\frac{5}{4x^4}\ +\ c$

4

$-\frac{1}{x^5}\ +\ c$

70

Multiple Choice

Integrate $\int_{ }^{ }3\ dx$

1

= 0

2

$=\frac{3}{x}+c$

3

$=\ 3x\ +c$

4

$=4+c$

71

Multiple Choice

Integrate $\int_{ }^{ }\cos\ \left(5x\right)\ dx$ with respect to x.

1

$\sin\ \left(5x\right)\ +\ c$

2

$-\frac{1}{5}\sin\ \left(5x\right)\ +\ c$

3

$\frac{1}{5}\ \sin\ \left(5x\right)\ +\ c$

4

$\frac{\cos\ \left(5x\right)}{5}\ +\ c$

72

Multiple Choice

Integrate $\sqrt{x}$ with respect to x

1

$x^{\frac{1}{2}}+c$

2

$\frac{1}{2}x^{-\frac{1}{2}}+\ c$

3

$\frac{2}{3}x^{\frac{3}{2}}+\ c$

4

$\frac{3}{2}x^{\frac{3}{2}}+\ c$

73

Multiple Choice

Which is the integral of $\int_{ }^{ }\ \left(5-3x\right)^3\ dx$ ?

1

$3\left(5-3x\right)^2\ +c$

2

$\frac{\left(5-3x\right)^4}{4}+\ c$

3

$\frac{\left(5-3x\right)^4}{12}+\ c$

4

$-\frac{\left(5-3x\right)^4}{12}+\ c$

74

Multiple Choice

Integrate $\int_{ }^{ }x^{\frac{1}{3}}dx$

1

$=\frac{4}{3}x^{\frac{4}{3}}+c$

2

$=\frac{3}{2}x^{\frac{2}{3}}+c$

3

$=\frac{1}{3}x^{-\frac{2}{3}}+c$

4

$=\frac{3}{4}x^{\frac{4}{3}}+c$

75

Multiple Choice

Which of the following is NOT one of techniques of Integration?

1

Substitution

2

By Part

3

Quotient Rule

4

Partial Fraction

76

Multiple Choice

What should be assigned to u in the integral?

1

2x²

2

sin (2x²)

3

5x

4

no u needed

77

Multiple Choice

Using integration by part, if given that u = (x + 1) then find v for $\int\left(x\ +1\right)\ e^{2x}\ dx$

1

$\frac{x^2}{2}+x$

2

$e^{2x}$

3

$2e^{2x}$

4

$\frac{e^{2x}}{2}$

78

Multiple Choice

$\int8x^{-3}dx$

1

$-2x^{-4}+C$

2

$4x^{-3}+C$

3

$\frac{8}{-3}x^{-2}$

4

$-4x^{-2}+C$

79

Multiple Choice

Integrate the partial fraction with respect to x
$\int_{ }^{ }\ \frac{1}{\left(x\right)}\ +\ \frac{4}{\left(2x\ -1\ \right)}\ dx$

1

$\ln\ \left|x\right|\ +\ 8\ \ln\left|2x-1\right|+c$

2

$\ln\ \left|x\right|\ +\ 4\ \ln\ \left|x-1\right|+c$

3

$\ln\ \left|x\right|\ +\ 4\ \ln\left|2x-1\right|+c$

4

$\ln\ \left|x\right|\ +\ 2\ \ln\left|2x-1\right|+c$

80

Multiple Choice

∫ (2 - x)⁵ dx

1

-5 (2 - x )⁴ + C

2

( 2 - x )⁶+ C

3

(1/6) ( 2 - x )⁶+ C

4

-(1/6) ( 2 - x )⁶+ C

81

Multiple Choice

Evaluate $\int_1^2\ \ 3x^2\ \ dx$

1

$7$

2

$8$

3

$12$

4

$x^3$

82

Multiple Choice

1

-1/x⁴+C

2

-x⁴+C

3

x^-4+C

4

-4/x⁴+C

83

Multiple Choice

Evaluate the integral $\int_0^2\ \frac{x^3\ +\ x^2}{x^2}\ dx$

1

$2$

2

$4$

3

$6$

4

$8$

84

Multiple Choice

∫ 2 x (x²- 3)^(1/2) dx

1

(x²- 3)^(3/2⁾+C

2

(3/2)(x²- 3)^(3/2)+C

3

(2/3)(x²- 3)^(3/2)+C

4

(2/3)(x²- 3)^(-1/2)+C

85

Multiple Choice

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

1

$\frac{ax^{n+1}}{n+1}$

2

$\frac{ax^{n-1}}{n-1}+\ c$

3

$\frac{ax^{n+1}}{n}+\ c$

4

$\frac{ax^{n+1}}{n+1}+\ c$

86

Multiple Choice

Which of the following is the indefinite integral of $\frac{3}{x^4}\ \ ?$

1

$-\frac{1}{x^3}+\ c$

2

$\frac{3}{5x^5}+\ c$

3

$-\frac{12}{x^5}+\ c$

4

$\frac{1}{x^3}+\ c$

87

Multiple Choice

∫ x (x² + 7 )^(1/3) dx

1

(3/4) ( x²+ 7 )^(4/3) + C

2

(3/8) ( x²+ 7 )^(4/3) + C

3

( x²+ 7 )^(4/3) + C

4

(3/2) ( x²+ 7 )^(4/3) + C

88

Multiple Choice

Find the integral:

1

1/3(x⁴ + 3)³ + c

2

1/12(x⁴ + 3)³ + c

3

3/4(x⁴ + 3)³ + c

4

1/4(x⁴ + 3)³ + c

89

Multiple Choice

∫ 2x cos(x²) dx

1

sin(2x) + C

2

2 sin ( 2x ) + C

3

(1/2) sin(2x) + C

4

4 cos(2x ) + C

90

Multiple Choice

Integrate $\int\left(2x+1\right)^{10}\ dx$ with respect to x.

1

$22\left(2x+1\right)^{11}+c$

2

$\frac{1}{22}\left(2x+1\right)^{11}+c$

3

$11\left(2x+1\right)^{10}+c$

4

$\frac{1}{11}\left(2x+1\right)^{10}+c$

91

Multiple Choice

∫ g ' ( x ) f (u) dx, u = g ( x )

1

∫ f ( u ) du

2

g ( x ) + C

3

( 1/ g ( x ) ) g ( x)⁴ + C

4

cannot be determined

92

Multiple Choice

Integrate $\int_{ }^{ }3\ dx$

1

= 0

2

$=\frac{3}{x}+c$

3

$=\ 3x\ +c$

4

$=4+c$

93

Multiple Choice

∫(3x⁴+2)⁴(12x³)dx

1

½(3x⁴+2)⁴+C

2

(3x⁴+2)⁴+C

3

⅕(3x⁴+2)⁵+C

4

⅓(3x⁴+2)⁶+C

94

Multiple Choice

$\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx$

1

$x^{-1}\ +\ x^{-2}+\ c$

2

$x^0\ -\ x^{-1}+\ c$

3

$\ln x+\ x^{-1}+\ c$

4

$\ln x-\ x^{-1}+\ c$

95

Multiple Choice

Solve for u-substitution: ∫x(x²-2)¹⁵ dx

1

((x²-2)¹⁶)/32 + C

2

(x²-2)¹⁶ + C

3

(x³-3)¹⁵ + C

96

Multiple Choice

Integrate $\int_{ }^{ }x^6dx$

1

$=6x^5+c$

2

$=\frac{x^7}{7}+c$

3

$=6x^6+c$

4

$=\frac{x^5}{6}+c$

97

Multiple Choice

What is the choice of u for ∫ e^x(1+e^x)^(1/2) dx?

1

e^x

2

1+e^x

3

(1+e^x)^(1/2)

4

(e^x)^(1/2)

98

Multiple Choice

$\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$

1

$\tan\ x\ \ +\ c$

2

$\frac{1}{5}\tan\ x\ \ +\ c$

3

$\frac{1}{5}\tan\ 5x\ \ +\ c$

4

$\frac{1}{5}\tan^2\ 5x\ \ +\ c$

99

Multiple Choice

Integrate $\int_{ }^{ }\left(\frac{1-\sin x}{\cos^2x}\right)dx$

1

$\tan x-\sec x+c$

2

$\tan x+\sec x+c$

3

$\cot x-\operatorname{cosec}x+c$

4

$\cot x+\operatorname{cosec}x+c$

100

Multiple Choice

Integrate $\int_{ }^{ }\left(x^2+7\right)dx$

1

$=2x+c$

2

$=x^3+7x$

3

$=\frac{1}{2}x^3+7x$

4

$=\frac{1}{3}x^3+7x+c$

101

Multiple Choice

Integrate $\int_{ }^{ }\left(\frac{\cos2x}{\cos^2x}\right)dx$

1

$2x-\tan x+c_{ }$

2

$2x+\tan x+c$

3

$x-\tan x+c$

4

$x+\tan x+c$

102

Multiple Choice

Integrate $\sin\left(\frac{x}{2}\right)$ with respect to x

1

$\cos\left(\frac{x}{2}\right)\ +\ c$

2

$-2\cos\left(\frac{x}{2}\right)\ +\ c$

3

$-\cos\left(\frac{x}{2}\right)\ +\ c$

4

$-\frac{1}{2}\cos\left(\frac{x}{2}\right)\ +\ c$

103

Multiple Choice

Integrate $\int_{ }^{ }\left(\frac{\cos^2x}{\sin^2x}\right)dx$

1

$-\cot x-x+c$

2

$\cot x+x+c$

3

$-\cot x+x+c$

4

$\cot x-x+c$

104

Multiple Choice

$\int6x\left(x+2\right)dx$

1

$6x^2+12x+C$

2

$x^{2\ }-2x+C$

3

$3x^2+6x+C$

4

$2x^3+6x^2+C$

105

Multiple Choice

Integrate $\int_{ }^{ }\left(\cos x-\sin x\right)^2dx$

1

$x+\frac{1}{2}\cos2x+c$

2

$x-\frac{1}{2}\cos2x+c$

3

$x+\cos2x+c$

4

$x-\cos2x+c$

106

Multiple Choice

Find the integral with respect to x of $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$

1

$\frac{e^{6x}}{6}\ +\ c$

2

$\frac{e^{9x}}{9}\ +\ c$

3

$6e^{6x}\ +\ c$

4

$\left(e^{3x}\right)^2\ +\ c$

107

Multiple Choice

Integrate $\int_{ }^{ }\frac{\left(1+\cos x\right)^2}{\sin^2x}dx$

1

$-2\cot x-x-2\operatorname{cosec}x+c$

2

$2\cot x-x+2\operatorname{cosec}x+c$

3

$-2\cot x-x+2\operatorname{cosec}x+c$

4

$2\cot x-x-2\operatorname{cosec}x+c$

108

Multiple Choice

Integrate $\int\left(2x+1\right)^{10}\ dx$ with respect to x.

1

$22\left(2x+1\right)^{11}+c$

2

$\frac{1}{22}\left(2x+1\right)^{11}+c$

3

$11\left(2x+1\right)^{10}+c$

4

$\frac{1}{11}\left(2x+1\right)^{10}+c$

109

Multiple Choice

Integrate $\int_{ }^{ }\left(\cot x-\tan x\right)^2dx$

1

$-\cot x-4x+\tan x+c$

2

$-\cot x-4x-\tan x+c$

3

$\cot x-4x-\tan x+c$

4

$\cot x-4x+\tan x+c$

110

Multiple Choice

Find indefinite integral for $\int_{ }^{ }\frac{1}{e^{5x}}\ dx$

1

$\frac{1}{5}e^{5x}\ +\ c$

2

$-5e^{4x}\ +\ c$

3

$\frac{e^{-5x}}{-5}+\ c$

4

$\frac{e^{-4x}}{-4}+\ c$

111

Multiple Choice

Integrate $\int_{ }^{ }\left(\cos x-\sec x\right)^2dx$

1

$-\frac{3}{2}x+\frac{1}{4}\sin2x+\tan x+c$

2

$-\frac{3}{2}x+\frac{1}{2}\sin2x+\tan x+c$

3

$-\frac{3}{2}x-\frac{1}{4}\sin2x+\tan x+c$

4

$-\frac{3}{2}x-\frac{1}{2}\sin2x+\tan x+c$

112

Multiple Choice

$\int5x^4dx$

1

$x^5$

2

$\frac{5}{4}x^5+C$

3

$x^5+C$

4

$20x^3$ + C

113

Multiple Choice

Integrate $\int_{ }^{ }\left(\frac{1+\cos x}{\sin^2x}\right)dx$

1

$-\cot x-\operatorname{cosec}x+c$

2

$-\cot x+\operatorname{cosec}x+c$

3

$\cot x+\operatorname{cosec}x+c$

4

$\cot x-\operatorname{cosec}x+c$

114

Multiple Choice

$\int\left(x^2-2x\right)dx$

1

$\frac{1}{3}x^3-x^2+C$

2

$x^{2\ }-2x+C$

3

$2x-2$

4

$\frac{1}{3}x^3-x^2$

115

Multiple Choice

Integrate $\int_{ }^{ }\left(\frac{\cos2x}{1-\cos^22x}\right)dx$

1

$-\frac{1}{2}\operatorname{cosec}2x+c$

2

$\frac{1}{2}\operatorname{cosec}2x+c$

3

$-\frac{1}{2}\sec2x+c$

4

$\frac{1}{2}\sec2x+c$

116

Multiple Choice

$\int\left(6\sqrt{x}-1\right)dx$

1

$6x^{\frac{3}{2}}+x+C$

2

$4x^{\frac{3}{2}}-x+C$

3

$3x^{-\frac{1}{2}}-x+C$

4

I didn't look at my notes to see how to do this one.

117

Multiple Choice

Evaluate the indefinite integral using integration by parts.
$\int3x\ e^{2x}\ dx\$

1

$-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C$

2

$\frac{3xe^{2x}}{2}-\frac{3e^{2x}}{4}+C$

3

$xe^{-2x}+\frac{\left(1-x^2\right)^{ }}{2}+C$

4

$-\frac{xe^{2x}}{2}+\frac{\ln e^{2x}}{4}+C$

118

Multiple Choice

$\int\left(\frac{1}{x^2}+\frac{6}{x^3}\right)dx$

1

$-x^{-1}-3x^{-2}+C$

2

$\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C$

3

$-x^{-1}-3x^{-2}$

4

$-x-3x^2+C$

119

Fill in the Blank

Evaluate antiderivative with respect to for

Cosecx

Type your answer in the boxes

120

Multiple Choice

$\int\left(5x^2-7x+6\right)dx$

1

$\frac{5}{3}x-\frac{7}{2}x+6x+C$

2

$x+x+x+x+x+C$

3

$x^3-3x^2+6x+C$

4

$\frac{5}{3}x^3-\frac{7}{2}x^2+6x+C$

121

Multiple Choice

Write antiderivative of -1/1+x² w.r to x

1

tan-¹x+C

2

Cot-¹x+C

3

tanx+C

122

Multiple Choice

$\int3x^5-\frac{1}{3}x^2\ dx$

1

$\frac{3x^5}{5}-\frac{1}{9}x^3+c$

2

$x^6-\frac{1}{3}x^3+c$

3

$\frac{1}{2}x^6-\frac{1}{3}x^3+c$

4

$\frac{1}{2}x^6-\frac{1}{9}x^3+c$

123

Multiple Choice

Antiderivative of ( logx)²/x w.r to x is

1

2logx/x² +C

2

(logx)³/3 +C

3

X+C

Integration

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