Free Printable integration

1.

∫(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

2.

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)

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

3.

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)

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

4.

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)

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

5.

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)

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

6.

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

a)

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

b)

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

c)

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

d)

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

7.

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)

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

8.

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)

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

9.

∫(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

10.

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

a)

= 0

b)

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

c)

$=\ 3x\ +c$

d)

$=4+c$

11.

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

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)

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

12.

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

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)

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

13.

∫ - sinx dx

a)

-cos x + C

b)

cos x + C

c)

tan x + C

d)

1/√1- x²

14.

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

a)

2ln|x+3|

b)

2ln(x + 3) + c

c)

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

d)

none of these

15.

∫ (2 - x)⁵ dx

a)

-5 (2 - x )⁴ + C

b)

( 2 - x )⁶+ C

c)

(1/6) ( 2 - x )⁶+ C

d)

-(1/6) ( 2 - x )⁶+ C

16.

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

17.

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

a)

$6x^2+12x+C$

b)

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

c)

$3x^2+6x+C$

d)

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

18.

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

a)

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

b)

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

c)

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

d)

$-x-3x^2+C$

19.

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

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)

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

20.

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

a)

$=\tan x+c$

b)

$=-\cos x+c$

c)

$=-\sec x+c$

d)

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

integration

Total questions: 20

Worksheet time: 48mins

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