## Definition

Integration is used to find areas, volumes, central points and often is used to find the area underneath the graph of a function.

## Common Functions of Integration

 Function Integral Constant ∫ a dx ax + c Variable ∫ x dx Square ∫ x2 dx Reciprocal ∫ (1/x) dx ln|x| + c Exponential ∫ ex dx ex + c ∫ ax dx ∫ ln(x) dx x ln(x) − x + c Trigonometry (x in radians) ∫ cos(x) dx sin(x) + c ∫ sin(x) dx -cos(x) + c ∫ sec2(x) dx tan(x) + c

## Rules of Integration

 Rules Function Integral Multiplication by constant ∫ cf(x) dx c∫f(x) dx Power Rule (n≠-1) ∫ xn dx Sum Rule ∫ (f + g) dx ∫f dx + ∫g dx Difference Rule ∫ (f – g) dx ∫f dx – ∫g dx

### Examples

 Rules Function Application Integral Multiplication by constant ∫ 5 cos(x) dx 5 ∫ cos(x) dx 5 sin(x) + c Power Rule (n ≠ -1) ∫ x2 dx Sum Rule ∫ (cos(x) + x2) dx ∫ cos(x) dx + ∫ x2 dx Difference Rule ∫ (x3 – sin(x)) dx ∫ x3 dx – ∫ sin(x) dx

## Learn More

Integration by Substitution (Reverse Chain Rule)

Common Derivatives

Differentiable

Implicit Differentiation

Calculus Index