Integration Formulas

Introduction to Integration: (lesson 1 of 2)

Here is a list of commonly used integration formulas. Applications of each formula can be found on the following pages.

$\int {{x^\gamma }dx = \frac{{{x^{\gamma + 1}}}}{r + 1} + C}$

1a:

$\int {kdx = kx + C}$

where $k$ is a constant

$\int {kf(x) = k\int {f(x)dx} }$

where $k$ is a constant

$\int {\left[ {f(x) + g(x)} \right]dx = \int {f(x)dx + \int {g(x)dx} } }$

$\int {{e^x}dx} = {e^x} + C$

$\int {{e^{f(x)}}} f'(x)dx = {e^{f(x)}} + C$

$\int {\frac{1}{x}dx = \ln \left| x \right| + C}$

$\int {\frac{{f'(x)}}{{f(x)}}dx = \ln \left| {f(x)} \right| + C}$

8: Integration by substitution

$\int {f(u)du = F(u) + C}$

where $u = g(x)$ and $du = g'(x)dx$

9: Integration by parts

$\int {f(x)g'(x)dx = f(x)g(x) - \int {f'(x)g(x)dx} }$

10:

$\int {\cos xdx = \sin x + C}$

11:

$\int {\left[ {\cos f(x)} \right]f'(x)dx = \sin f(x) + C}$

12:

$\int {\sin xdx = - \cos x + C}$

13:

$\int {\left[ {\sin f(x)} \right]f'(x)dx = - \cos f(x) + C}$

14:

$\int {{{\sec }^2}xdx} = \tan x + C$

15:

$\int {\left[ {{{\sec }^2}f(x)} \right]} f'(x)dx = \tan f(x) + C$

Algebra

It is a mathematical fact that fifty percent of all doctors graduate in the bottom half of their class.

Author Unknown

God created the natural number, and all the rest is the work of man.

Leopold Kronecker