Learn – Calculus – Integration techniques

1 Of algebraic functions
- 1.1 Exercises
2 Of trigonometric functions
- 2.1 Exercises

Of algebraic functions

Exercises

Problem set

Evaluate the following.

$\int \frac{3}{x+1} + \frac{5}{x-1} \, dx$
$\int \frac{1}{(x+1)(x+3)} \, dx$
$\int \frac{1}{1-x^2}\,dx$
$\int \frac{1}{16-x^2}\,dx$
$\int \frac{2}{x^2-4x+3} \, dx$
$\int \frac{8x-1}{2x^2-3x-2} \, dx$

Problem set

Evaluate the following.

$\int \frac{1}{\sqrt{1-x^2}}\,dx$
$\int \frac{1}{1+x^2}\,dx$
$\int \frac{1}{\sqrt{9-x^2}}\,dx$
$\int \frac{1}{25+x^2}\,dx$
$\int \frac{1}{x^2+10}\,dx$

Problem set

Evaluate the following.

$\int \frac{1}{x^2+4x+9}\,dx$
$\int \frac{1}{x^2-10x+10}\,dx$
$\int \frac{3}{x^2+7x+4}\,dx$
$\int \frac{7}{3x^2-12x-2}\,dx$
$\int \frac{5}{2x^2+6x+5}\,dx$

Problem set

Evaluate the following.

$\int \frac{2x+5}{x^2+5x+11}\,dx$
$\int \frac{6x-7}{3x^2-7x+3}\,dx$
$\int \frac{x}{5x^2+10x+9}\,dx$
$\int \frac{x+5}{4x^2+8x-9}\,dx$
$\int \frac{3x-4}{10x^2-20x-1}\,dx$

Problem set

Evaluate the following.

$\int \frac{x^2}{\sqrt{9-x^2}}\,dx$
$\int \frac{1}{\sqrt{25+x^2}}\,dx$
$\int \frac{1}{\sqrt{x^2-4}}\,dx$

Of trigonometric functions

Exercises

Problem set

Evaluate the following.

$\int \tan x\,dx$
$\int \sec x\,dx$
$\int \cot x\,dx$
$\int \csc x\,dx$

Problem set

Evaluate the following.

$\int \sin^3 x\,dx$
$\int \cos^5 x\,dx$
$\int \sin^2 x\,dx$
$\int \cos^4 x\,dx$

Problem set

Evaluate the following.

$\int \sin^2 x\cos^3 x\,dx$
$\int \sin^3 x\cos^4 x\,dx$
$\int \sin^2 x\cos^2 x\,dx$
$\int \sin^4 x\cos^4 x\,dx$