Free Printable Integration

1.

Evaluate this integral....

a)

b)

c)

d)

2.

Evaluate this integral....

a)

b)

c)

d)

3.

Evaluate this integral....

a)

b)

c)

d)

4.

Evaluate this integral....

a)

b)

c)

d)

5.

Evaluate the integral.....

a)

b)

c)

d)

6.

Evaluate the integral.....

a)

b)

c)

d)

7.

Evaluate the integral.....

a)

b)

c)

d)

8.

Evaluate the integral.....

a)

b)

c)

d)

9.

What is the integral of sin x with respect to x.

a)

cos x

b)

-cos x

c)

cos x + C

d)

-cos x + C

10.

What is the integral of cosec²x with respect x?

a)

-cot x + C

b)

cot x + C

c)

cos x + C

d)

-cos x + C

11.

What is the integral of cos x with respect to x ?

a)

-sin x

b)

sin x

c)

-sin x + C

d)

sin x + C

12.

What is the integral of 1/u with respect to u?

a)

1/u² + C

b)

log u

c)

log u + C

d)

-1/u² + C

13.

What is the integral of sec²z with respect to z?

a)

tan z

b)

tan z + C

c)

sec z tan z + C

d)

sec z tan z

14.

What is the integral of dx/(√(1-x²) ?

a)

arctan x + C

b)

arccos x + C

c)

arcsin x + C

d)

arcsec x + C

15.

What is the integral of sec u tan u du?

a)

tan u + C

b)

sec u + C

c)

sec²u + C

d)

tan²u + C

16.

What is the integral of cosec x cot x with respect to x?

a)

-cosec x + C

b)

cosec x +C

c)

cot x + C

d)

-cot x +C

17.

$\int4x^7dx$

a)

$\frac{1}{8}x^8+c$

b)

$\frac{1}{2}x^8+c$

c)

$\frac{1}{8}x^8$

d)

$28x^8+c$

18.

$\int\left(5x^2-2\sin x\right)\ dx$

a)

$\frac{3}{5}x^3+2\cos x+c$

b)

$\frac{3}{5}x^3-2\cos x+c$

c)

$\frac{5}{3}x^3+2\cos x+c$

d)

$\frac{5}{3}x^3-2\cos x+c$

19.

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

a)

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

b)

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

c)

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

d)

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

20.

$\int\tan x_{ }dx\$

a)

$\ln\left|\cos\right|+C$

b)

$-\ln\left|\cos x\right|+C$

c)

$\ln\left|\sin x\right|+c$

d)

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

21.

\int_{ }^{ }\left(e^x\right)dx=

a)

$e^x+C$

b)

$x+C$

c)

$0$

d)

none of these

22.

\int_{ }^{ }\sec x\tan x\ dx=

a)

$\sec\ x+C$

b)

$\sec^2x+C$

c)

$\tan\ x+C$

d)

$\tan^2x+C$

23.

\int_{ }^{ }\left(\frac{1}{1+x^2}\right)dx=

a)

$\sin^{-1}x+C$

b)

$\tan x+C$

c)

$\tan^{-1}x+C$

d)

$\cot^{-1}x+C$

24.

\int_{ }^{ }\left(a^x\right)dx=

a)

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

b)

$a^x\log a+C$

c)

$a^x+C$

d)

none of these

25.

\int_{ }^{ }\left(\operatorname{cosec}^2x\right)dx=

a)

$\cot x+C$

b)

$-\cot x+C$

c)

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

d)

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

26.

\int_{ }^{ }\left(e^x\right)dx=

a)

$e^x+C$

b)

$x+C$

c)

$0$

d)

none of these

27.

\int_{ }^{ }\left(\cos x\right)dx=

a)

$\sin x+C$

b)

$-\sin x+C$

c)

$\cos x+C$

d)

none of these

28.

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

a)

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

b)

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

c)

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

d)

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

29.

\int_{ }^{ }\left(\frac{1}{x\sqrt{x^2-1}}\right)dx=

a)

$\operatorname{cosec}^{-1}x+C$

b)

$\sec^{-1}x+C$

c)

$\cot^{-1}x+C$

d)

none of these

30.

∫ 1/x dx

a)

ln x

b)

ln x + C

c)

-1/x²

d)

-1/x² + C

31.

Find $\int_{ }^{ }\sin x\ \ dx$

a)

$=-\cos x+c$

b)

$=\sec^2x+c$

c)

$=\cos x+c$

d)

$=-\sin x+c$

32.

Find $\int_{ }^{ }\sec^2x\ dx$

a)

$=\tan x+c$

b)

$=-\cos^2x+c$

c)

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

d)

$=-\frac{1}{\sin x}+c$

33.

What is the integral of 1/(√(1-x²)

a)

arctan x + C

b)

arccosx + C

c)

arcsinx + C

d)

secx + C

34.

\int_{ }^{ }\left(\operatorname{cosec}^2x\right)dx=

a)

$\cot x+C$

b)

$-\cot x+C$

c)

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

d)

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

35.

\int_{ }^{ }\left(e^x\right)dx=

a)

$e^x+C$

b)

$x+C$

c)

$0$

d)

none of these

36.

\int_{ }^{ }\left(\cos x\right)dx=

a)

$\sin x+C$

b)

$-\sin x+C$

c)

$\cos x+C$

d)

none of these

37.

$\int dx=$

a)

$0$

b)

$x+C$

c)

$1$

d)

$undefined$

38.

what is the integral of cosecx cotx

a)

cosecx +C

b)

-cosecx +C

c)

cotx +C

d)

-cotx +C

39.

Find the integral:

a)

1/3(x⁴ + 3)³ + c

b)

1/12(x⁴ + 3)³ + c

c)

3/4(x⁴ + 3)³ + c

d)

1/4(x⁴ + 3)³ + c

40.

Find the integral:

a)

1/8(4x² + 3)⁴ + c

b)

1/2(4x² + 3)⁴ + c

c)

1/32(4x² + 3)⁴ + c

d)

1/4(4x² + 3)⁴ + c

41.

Find the integral:

a)

-1/3 (16 - x³)^-1+ c

b)

1/3 (16 - x³)^-1+ c

c)

- (16 - x³)^-1+ c

d)

-1/2 (16 - x³)^-2+ c

42.

Find the integral:

a)

1/3 (x³ + 2)^3/2 + c

b)

1/2 (x³ + 2)^-1/2 + c

c)

2/3 (x³ + 2)^3/2 + c

d)

2/9 (x³ + 2)^3/2 + c

43.

What is substitution u for in the integrand given?

a)

b)

c)

d)

44.

∫(3x⁴+2)⁴(12x³)dx

a)

½(3x⁴+2)⁴+C

b)

(3x⁴+2)⁴+C

c)

⅕(3x⁴+2)⁵+C

d)

⅓(3x⁴+2)⁶+C

45.

∫3x³√(x⁴+3)dx

a)

¾(x⁴+3)^3/2 + C

b)

¾x⁴(⅕x⁵ +3x) + C

c)

½(x⁴+3)^3/2+ C

d)

None of these

46.

a)

ln(2x²+6) + C

b)

ln(2x²+6)(4x) + C

c)

1/(2x²+6) + C

d)

1/(2x²+6)²+ C

47.

∫ e^2x dx

a)

e^2x +C

b)

2e^2x + C

c)

(1/2)e^{x + C}

d)

(1/2)e^2x +C

48.

∫5 e^5x dx

a)

25 e^5x + C

b)

5 e^{5x - 1} + C

c)

e^5x + C

d)

(1/5) e^5x+ C

49.

a)

-4x⁶-5x²+C

b)

-24x⁶-10x²+C

c)

-4x⁵-5x+C

d)

-4x⁶-10+C

50.

\int_{ }^{ }\left(\cos x\right)dx=

a)

$\sin x+C$

b)

$-\sin x+C$

c)

$\cos x+C$

d)

none of these

51.

What is an antiderivative?

a)

The opposite of a derivative

b)

The same as a derivative

c)

A second derivative

d)

It always represents velocity.

52.

What does C represent in an antiderivative?

a)

A variable

b)

A constant

c)

None of these

d)

Unknown

53.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

54.

∫ 2 x (x²- 3)^(1/2) dx

a)

(x²- 3)^(3/2)+C

b)

(3/2)(x²- 3)^(3/2)+C

c)

(2/3)(x²- 3)^(3/2)+C

d)

(2/3)(x²- 3)^(-1/2)+C

55.

∫ 6 x (x² +1 )² dx

a)

( x² + 1)³ + C

b)

3 ( x² + 1)³ + C

c)

( x² + 1)¹ + C

d)

6 ( x² + 1)³ + C

56.

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

a)

= 0

b)

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

c)

$=\ 3x\ +c$

d)

$=4+c$

57.

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

a)

$=6x^5+c$

b)

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

c)

$=6x^6+c$

d)

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

58.

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

a)

$=2x+c$

b)

$=x^3+7x$

c)

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

d)

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

59.

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

a)

$=\ln2x+c$

b)

$=2\ \ln2x+c$

c)

$=\frac{1}{2}\ln2x+c$

d)

$=\frac{1}{\ln2x}+c$

60.

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

a)

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

b)

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

c)

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

d)

$4\ln\left|x\right|+e^x+C$

61.

$\int\cos\left(3-4x\right)dx_{ }^{ }$

a)

$\frac{1}{4}\sin\left(3-4x\right)+C$

b)

$4\sin\left(3-4x\right)+C$

c)

$-\frac{1}{4}\sin\left(3-4x\right)+C$

d)

$-4\sin\left(3-4x\right)+C$

62.

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

a)

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

b)

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

c)

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

d)

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

63.

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

a)

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

b)

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

c)

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

d)

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

64.

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

a)

$6x^2+12x+C$

b)

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

c)

$3x^2+6x+C$

d)

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

65.

∫ - sinx dx

a)

-cos x + C

b)

cos x + C

c)

tan x + C

d)

1/√1- x²

66.

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

a)

$e^{5x}+c$

b)

$5e^{5x}+c$

c)

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

d)

none of these

67.

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

a)

2ln|x+3|

b)

2ln(x + 3) + c

c)

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

d)

none of these

68.

∫(cos x + 3x²)dx =

a)

-sin x + x³ + c

b)

sinx + x³ + c

c)

-sin x + 6x

d)

🌞

69.

∫ 1/x dx

a)

ln x

b)

ln x + C

c)

-1/x²

d)

-1/x² + C

70.

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

a)

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

b)

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

c)

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

d)

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

71.

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

a)

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

b)

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

c)

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

d)

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

72.

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

a)

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

b)

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

c)

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

d)

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

73.

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

a)

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

b)

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

c)

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

d)

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

74.

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

a)

$\tan\ x\ \ +\ c$

b)

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

c)

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

d)

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

75.

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

a)

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

b)

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

c)

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

d)

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

76.

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

a)

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

b)

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

c)

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

d)

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

77.

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

a)

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

b)

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

c)

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

d)

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

78.

$\int5x^4dx$

a)

$x^5$

b)

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

c)

$x^5+C$

d)

$20x^3$ + C

79.

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

a)

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

b)

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

c)

$2x-2$

d)

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

80.

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

a)

$6x^2+12x+C$

b)

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

c)

$3x^2+6x+C$

d)

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

81.

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

a)

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

b)

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

c)

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

d)

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

82.

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

a)

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

b)

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

c)

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

d)

$-x-3x^2+C$

83.

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

a)

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

b)

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

c)

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

d)

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

84.

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

a)

$=\tan x+c$

b)

$=-\cos x+c$

c)

$=-\sec x+c$

d)

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

85.

∫(cos x + 3x²)dx =

a)

-sin x + x³ + c

b)

sinx + x³ + c

c)

-sin x + 6x

d)

🌞

86.

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

a)

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

b)

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

c)

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

d)

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

87.

a)

⅝

b)

-⅝

c)

⅜

d)

45/16

88.

∫e^xsin(e^x+6) dx

a)

-cos(e^x+6) + C

b)

cos(e^x+6) +C

c)

sin(e^x+6)+C

d)

e^2x/2

89.

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

a)

2ln|x+3| + c

b)

2ln(x + 3) + c

c)

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

d)

none of these

90.

∫cos(4x+5)dx

a)

-¼sin(4x + 5) + C

b)

4sin(4x + 5) + C

c)

¼sin(4x + 5) + C

d)

4cos(4x + 5) + C

91.

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

a)

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

b)

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

c)

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

d)

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

92.

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

a)

$\tan x-\sec x+c$

b)

$\tan x+\sec x+c$

c)

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

d)

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

93.

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

a)

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

b)

$2x+\tan x+c$

c)

$x-\tan x+c$

d)

$x+\tan x+c$

94.

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

a)

$-\cot x-x+c$

b)

$\cot x+x+c$

c)

$-\cot x+x+c$

d)

$\cot x-x+c$

95.

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

a)

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

b)

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

c)

$x+\cos2x+c$

d)

$x-\cos2x+c$

96.

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

a)

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

b)

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

c)

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

d)

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

97.

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

a)

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

b)

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

c)

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

d)

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

98.

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

a)

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

b)

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

c)

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

d)

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

99.

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

a)

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

b)

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

c)

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

d)

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

100.

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

a)

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

b)

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

c)

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

d)

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

101.

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

a)

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

b)

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

c)

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

d)

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

102.

∫cos(4x+5)dx

a)

-¼sin(4x + 5) + C

b)

4sin(4x + 5) + C

c)

¼sin(4x + 5) + C

d)

4cos(4x + 5) + C

103.

a)

-60x^-5 - 40x^-6 + C

b)

-45x^-3 - 32x^-4 + C

c)

15x^-3 + 8x^-4 + C

d)

-5x^-3 - 2x^-4 + C

104.

a)

62

b)

64/11

c)

56/3

d)

50/3

105.

a)

3

b)

½

c)

-3/2

d)

4/11

106.

a)

A

b)

B

c)

C

d)

D

107.

a)

A

b)

B

c)

C

d)

D

108.

a)

A

b)

B

c)

C

d)

D

109.

Choose the best strategy to use when finding

\int\left(\frac{x}{x^2-49}\right)dx

a)

U-substitution

b)

Integration by parts

c)

Partial fractions

d)

Adding/subtracting terms in the numerator

e)

Dividing out

110.

Choose the best strategy to use when finding

\int\left(\frac{100}{\sqrt{100-x^2}}\right)dx

a)

U-substitution

b)

Basic integration formulas

c)

Completing the square

d)

Adding/subtracting terms in the numerator

e)

Rationalize the denominator

111.

Choose the best strategy to use when finding

\int\left(\frac{x^2}{e^x}\right)dx

a)

U-substitution

b)

Integration by parts

c)

Partial Fractions

d)

Adding/subtracting terms in the numerator

e)

Basic integration formula

112.

Choose the best strategy to use when finding

\int\left(\frac{2x}{9+x^4}\right)dx

a)

U-substitution

b)

Integration by parts

c)

Partial Fractions

d)

Adding/subtracting terms in the numerator

e)

Basic integration formula

113.

Choose the best strategy to use when finding

\int\left(\frac{3}{9-x^2}\right)dx

a)

U-substitution

b)

Integration by parts

c)

Partial Fractions

d)

Adding/subtracting terms in the numerator

e)

Basic integration formula

114.

$\int\frac{3}{2}\ dx$

a)

$0$

b)

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

c)

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

d)

$3x^2+c$

115.

Given $\frac{d}{dx}\left(\frac{2}{x-3}\right)=g\left(x\right)$ , find $\int_{ }^{ }g\left(x\right)dx$ .

a)

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

b)

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

c)

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

d)

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

116.

$\int_{ }\left(2x+5\right)^3dx$

a)

$\frac{\left(2x+5\right)^4}{8}$

b)

$\frac{\left(2x+5\right)^4}{8}+c$

c)

$\frac{\left(2x-5\right)^4}{8}+c$

d)

$\frac{\left(2x+5\right)^3}{8}+c$

117.

$\int_{ }\frac{8}{x^5}dx$

a)

$-\frac{2}{x^4}$

b)

$\frac{2}{x^4}+c$

c)

$-\frac{2}{x^4}+c$

d)

$\frac{2}{x^4}$

118.

$\int_{ }\frac{2}{3}\sqrt{x}dx$

a)

$\frac{4}{9}x^{\frac{3}{2}}$

b)

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

c)

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

d)

$\frac{4}{9}x^{\frac{3}{2}}+c$

119.

$\int_{ }8e^{7+2x}dx$

a)

$8\left(\frac{e^{7+^{ }2x}}{2\left(\ln e\right)}\right)$

b)

$8\left(\frac{e^{7+^{ }2x}}{\left(\ln e\right)}\right)+c$

c)

$8\left(\frac{e^{7+^{ }2x}}{2\left(\ln e\right)}\right)+c$

d)

$\left(\frac{e^{7+^{ }2x}}{2\left(\ln e\right)}\right)+c$

120.

$\int_1^24^xdx$

a)

$\frac{12}{\ln4}$

b)

$\frac{\ln4}{12}$

c)

2.3336

d)

4.114

121.

$\int_{ }\frac{4}{5x-6}dx$

a)

$4\ln\left|5x-6\right|+c$

b)

$\frac{4}{5}\ln\left|5x-6\right|+c$

c)

$\frac{4}{5}\ln\left|5x-6\right|$

d)

$\ln\left|5x-6\right|+c$

122.

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

a)

$-\frac{\ln2}{2}$

b)

$\frac{\ln2}{2}$

c)

$-\ln2$

d)

$\ln2$

123.

$\int_{ }\frac{2x+1}{x^2+x+1}dx$ by using method of substitution.

a)

$\ln\left|u\right|$

b)

$\ln\left|u\right|+c$

c)

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

d)

$\ln\left|x^2+x+1\right|$

124.

$\int_{ }\frac{\left(\ln3x\right)^4}{x}dx$ by using method of substitution.

a)

$\frac{u^5}{5}$

b)

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

c)

$\ln3x+c$

d)

$\frac{\ln3x}{5}+c$

125.

$\int_{ }^{ }\sin\left(2x+3\right)dx$

a)

$\frac{-\cos\left(2x+3\right)}{2}$

b)

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

c)

$\frac{-\cos\left(2x+3\right)}{2}+c$

d)

$\frac{\cos\left(2x+3\right)}{2}+c$

126.

$\int_{ }\left(3\tan x+4\right)^5\sec^2x\ dx$ by using method of substitution.

a)

$\left(3\tan x\ +4\right)^6+c$

b)

$\frac{\left(3\tan x\ +4\right)^6}{6}$

c)

$\frac{\left(3\tan x\ -4\right)^6}{6}+c$

d)

$\frac{\left(3\tan x\ +4\right)^6}{6}+c$

127.

$\int_{ }xe^x\ dx$ by using integration by parts.

a)

$e^x\left(x-1\right)+c$

b)

$xe^x+e^x+c$

c)

$xe^x+c$

d)

$xe^x-e^x$

128.

$\int_{ }x\sin x\ dx$ by using integration by parts.

a)

$x\cos x+\sin x+c$

b)

$-x\cos x+\sin x+c$

c)

$-x\sin x+\cos x+c$

d)

$-x\cos x+\sin x$

129.

Find $\int_{ }^{ }\sin3x\ \ dx$

a)

$=-\frac{1}{3}\cos3x+c$

b)

$=\cos3x+c$

c)

$=3\cos3x+c$

d)

$=\frac{1}{3}\cos x+c$

130.

Find $\int_{ }^{ }\sec^25x\ dx$

a)

$=\frac{1}{5}\tan5x+c$

b)

$=\tan^25x+c$

c)

$=\frac{\tan^25x}{5}+c$

d)

$=\frac{5}{\cos^25x}+c$

131.

Find $\int_{ }^{ }\sin\left(1-3x\right)\ \ dx$

a)

$=\frac{1}{3}\cos\left(1-3x\right)+c$

b)

$=-\cos\left(1-3x\right)+c$

c)

$=3\cos\left(1-3x\right)+c$

d)

$=-\frac{1}{3}\cos\left(1-3x\right)+c$

132.

Find $\int_{ }^{ }\cos\left(2x+3\right)\ \ dx$

a)

$=\frac{1}{2}\sin\left(2x+3\right)+c$

b)

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

c)

$=-2\sin\left(2x+3\right)+c$

d)

$=-\frac{1}{2}\sec^2\left(2x+3\right)+c$

133.

Find $\int_{ }^{ }\sec^2\left(5x-2\right)\ dx$

a)

$=\frac{1}{5}\tan\left(5x-2\right)+c$

b)

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

c)

$=\frac{\tan^2\left(5x-2\right)}{5}+c$

d)

$=-\frac{5}{\tan\left(5x-2\right)}+c$

134.

Find $\int_{ }^{ }\cos\left(x+\pi\right)\ \ dx$

a)

$=\sin\left(x+\pi\right)+c$

b)

$=-\sin x-\sin\pi+c$

c)

$=\pi\sin\left(x+\pi\right)+c$

d)

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

135.

a)

Power Rule

b)

Trig Memory

c)

U-Subs

d)

Partial Fractions

e)

Parts

136.

a)

Power Rule

b)

Trig Memory

c)

U-Subs

d)

Partial Fractions

e)

Parts

137.

a)

Power Rule

b)

Trig Memory

c)

U-Subs

d)

Partial Fractions

e)

Parts

138.

a)

Power Rule

b)

Trig Memory

c)

U-Subs

d)

Partial Fractions

e)

Parts

139.

a)

Power Rule

b)

Trig Memory

c)

U-Subs

d)

Partial Fractions

e)

Parts

140.

a)

Power Rule

b)

Trig Memory

c)

U-Subs

d)

Partial Fractions

e)

Parts

141.

$\frac{d}{dx}\left[uv\right]$

a)

$u'v+v'u$

b)

$u'v-v'u$

c)

$\frac{u'v-v'u}{v^2}$

d)

$\frac{u'v+v'u}{v^2}$

142.

Which of the following is TRUE ?

a)

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

b)

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

c)

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

d)

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

143.

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

a)

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

b)

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

c)

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

d)

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

144.

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

a)

Substitution

b)

By Part

c)

Quotient Rule

d)

Partial Fraction

145.

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

a)

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

b)

$e^{2x}$

c)

$2e^{2x}$

d)

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

146.

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

a)

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

b)

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

c)

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

d)

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

147.

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

a)

$7$

b)

$8$

c)

$12$

d)

$x^3$

148.

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

a)

$2$

b)

$4$

c)

$6$

d)

$8$

Integration

Total questions: 148

Worksheet time: 4hrs 47mins

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