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Introduction to Integration: (lesson 1 of 2)

## Integration Formulas

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

1:

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

1a:

$\int {kdx = kx + C}$

where $k$ is a constant

2:

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

where $k$ is a constant

3:

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

4:

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

5:

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

6:

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

7:

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

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:

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