Free Printable Integration by Substitution

1.

∫ 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

2.

$\int\ 4x^3\left(x^4-1\right)^2\ dx$

a)

$\left(x^4-1\right)^3+c$

b)

$\frac{1}{3}\left(x^4-1\right)^3+c$

c)

$\frac{4}{3}\left(x^4-1\right)^3+c$

d)

$4\left(x^4-1\right)^3+c$

3.

Integrate $\int7x^6\left(x^7+1\right)^8dx$

a)

$\frac{\left(x^7-1\right)^9}{9}+c$

b)

$\frac{\left(x^7+1\right)^9}{9}+c$

c)

$\frac{\left(x^7+1\right)^8}{8}+c$

d)

$\frac{\left(7x^6+1\right)^9}{9}+c$

4.

Choose correct 'u' for u-substitution method:
$\int\left(\frac{2x+1}{x^2+x-2}\right)dx$

a)

Let $u=2x+1$

b)

Let $u=x^2$

c)

Let $u=x^2+x-2$

d)

Let $u=dx$

5.

$\int10x^2\left(5x^2-4\right)^3dx$

a)

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

b)

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

c)

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

d)

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

6.

$\int15x^4\sqrt{3x^5-2}dx$

a)

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

b)

$3x^5\sqrt{\frac{1}{2}x^6-2x}+C$

c)

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

d)

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

7.

Use the indicated substitution to evaluate the integral.

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

a)

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

b)

$\sqrt{3+x^2}+C$

c)

$2\sqrt{3+x^2}+C$

d)

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

8.

Use substitution to evaluate the integral $\int\frac{2x}{\left(x^2+3\right)^3}\ dx$

a)

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

b)

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

c)

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

d)

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

9.

Use substitution to evaluate the integral $\int\left(3x^3+5\right)^5\cdot27x^2dx$

a)

$\frac{1}{2}\left(3x^3+5\right)^6+C$

b)

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

c)

$\frac{5}{6}\left(3x^3+5\right)^6+C$

d)

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

10.

Use substitution to evaluate the integral

$\int\ x^2\sqrt{5+2x^3}\ dx$

a)

$\frac{1}{9}\left(5+2x^3\right)^{\frac{3}{2}}+C$

b)

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

c)

$6x\left(5+2x^3\right)^{\frac{3}{2}}+C$

d)

$\frac{1}{9}x^3\left(5+2x^3\right)^{\frac{3}{2}}+C$

Integration by Substitution

Total questions: 10

Worksheet time: 50mins

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