Free Printable Basic Integration

1.

$\int3\ dx$

a)

$3x+c$

b)

$x^3+c$

c)

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

d)

$3x^2+c$

2.

$\int x^5\ dx$

a)

$x^6+c$

b)

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

c)

$5x^4+c$

d)

$6x^6+c$

3.

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

a)

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

b)

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

c)

$2\sqrt{x}+c$

d)

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

4.

$\int\ x^{\frac{1}{3}}\ dx$

a)

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

b)

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

c)

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

d)

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

5.

$\int\ 6x^2\ dx$

a)

$2x^3+c$

b)

$3x^3+c$

c)

$12x^3+c$

d)

$2x^2+c$

6.

$\int\ x+6\ dx$

a)

$x^2+6x+c$

b)

$\frac{x^2}{2}+6x+c$

c)

$\frac{x^2}{2}+6+c$

d)

$2x^2+6x+c$

7.

$\int\ 3x+9\ dx$

a)

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

b)

$3x^2+9x+c$

c)

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

d)

$2x^2+9x+c$

8.

$\int\ 2x^3+2x+7\ dx$

a)

$2x^4+x^2+7x+c$

b)

$\frac{6x^4}{4}+2x^2+7x+c$

c)

$\frac{x^4}{4}+\frac{x^2}{2}+7x+c$

d)

$\frac{x^4}{2}+x^2+7x+c$

9.

$\int\ x-2\ dx$

a)

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

b)

$2x^2-2x+c$

c)

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

d)

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

10.

$\int\ \frac{1}{\sqrt{2}}-x\ dx$

a)

$\sqrt{2}-2x+c$

b)

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

c)

$\sqrt{2}x-2x+c$

d)

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

11.

$\int\ 3x-7x^2\ dx$

a)

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

b)

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

c)

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

d)

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

12.

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

a)

$\frac{2x^3}{9}+\frac{x^2}{4}-5x+c$

b)

$\frac{9x^3}{2}-4x^2-5x+c$

c)

$\frac{2x^2}{9}-\frac{x^3}{4}-5x+c$

d)

$\frac{2x^3}{9}-\frac{x^2}{4}-5x+c$

13.

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

a)

$\frac{x^5}{5}-\frac{3x^4}{4}+c$

b)

$5x^5-\frac{3x^4}{4}+c$

c)

$\frac{x^5}{5}+\frac{3x^4}{4}+c$

d)

$\frac{x^5}{5}-\frac{4x^4}{3}+c$

14.

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

a)

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

b)

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

c)

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

d)

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

15.

$\int\ \frac{x^2+1}{\sqrt{x}}\ dx$

a)

$\frac{2}{5}x^{\frac{2}{5}}+2\sqrt{x}+c$

b)

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

c)

$\frac{2}{5}x^{\frac{5}{2}}+2\sqrt{x}+c$

d)

$\frac{5}{2}x^{\frac{5}{2}}+2\sqrt{x}+c$

16.

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

a)

$-\frac{4}{x}-8\sqrt{x}-\frac{x^2}{2}+c$

b)

$\frac{4}{x}+8\sqrt{x}+\frac{x^2}{2}+c$

c)

$-\frac{4}{x}+8\sqrt{x}+\frac{x^2}{2}+c$

d)

$-\frac{4}{x}-8\sqrt{x}+\frac{x^2}{2}+c$

17.

$\int\ \left(4x+7\right)^5\ dx$

a)

$\frac{\left(4x+7\right)^6}{24}+c$

b)

$\frac{\left(4x+7\right)^6}{6}+c$

c)

$\frac{\left(4x+7\right)^6}{4}+c$

d)

$\frac{5\left(4x+7\right)^4}{30}+c$

18.

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

a)

$\frac{1}{8}\left(1-2x\right)^4+c$

b)

$-\frac{1}{8}\left(1-2x\right)^4+c$

c)

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

d)

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

19.

$\int\ \left(3-6x\right)^{-4}\ dx$

a)

$-\frac{1}{18}\left(3-6x\right)^{-3}+c$

b)

$\frac{1}{30}\left(3-6x\right)^{-5}+c$

c)

$\frac{1}{18}\left(3-6x\right)^{-3}+c$

d)

$-\frac{1}{3}\left(3-6x\right)^{-3}+c$

20.

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

a)

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

b)

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

c)

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

d)

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

21.

$\int\ \sqrt{1+4x}\ dx$

a)

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

b)

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

c)

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

d)

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

22.

$\int\ \left(1-x\right)^{-\frac{1}{2}}\ dx$

a)

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

b)

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

c)

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

d)

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

23.

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

a)

$\frac{20}{3}\left(5x+2\right)^{\frac{4}{3}}+c$

b)

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

c)

$\frac{3}{20}\left(5x+2\right)^{\frac{4}{3}}+c$

d)

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

Basic Integration

Total questions: 23

Worksheet time: 12mins

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