Integration

Indefinite Integrals

For calculating integrals of ordinary polynomials of x to a power use the following basic formula:

picture = picture     Where c is an unknown constant without a variable attached to it.

If you check by taking the derivative of picture   you will see that you are left with picture. This can be thought of in two steps.

  1. Increase the exponent by 1
  2. Divide by the new exponent

For example

1.1   picture picture

1.2   picture picture

1.3   picture picture

1.4   picture picture

1.5   picture picture

1.6   picture picture

Integrals of trigonometric functions work the exact opposite of derivatives. The derivative of picture so the integral of picture.

picture
picture
picture
picture
picture
picture

For example:

1.7   picture picture

1.8   picture picture

1.9   picture picture

1.10  picture picture

1.11  picture picture