Learn – Calculus – Integration techniques

1 Of algebraic functions

1.1 Exercises

1.1.1 Problem set

Evaluate the following.

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

1.1.2 Problem set

Evaluate the following.

  1. \int \frac{1}{\sqrt{1-x^2}}\,dx
  2. \int \frac{1}{1+x^2}\,dx
  3. \int \frac{1}{\sqrt{9-x^2}}\,dx
  4. \int \frac{1}{25+x^2}\,dx
  5. \int \frac{1}{x^2+10}\,dx

1.1.3 Problem set

Evaluate the following.

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

1.1.4 Problem set

Evaluate the following.

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

1.1.5 Problem set

Evaluate the following.

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

2 Of trigonometric functions

2.1 Exercises

2.1.1 Problem set

Evaluate the following.

  1. \int \tan x\,dx
  2. \int \sec x\,dx
  3. \int \cot x\,dx
  4. \int \csc x\,dx

2.1.2 Problem set

Evaluate the following.

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

2.1.3 Problem set

Evaluate the following.

  1. \int \sin^2 x\cos^3 x\,dx
  2. \int \sin^3 x\cos^4 x\,dx
  3. \int \sin^2 x\cos^2 x\,dx
  4. \int \sin^4 x\cos^4 x\,dx