Integration

Integration reverses differentiation. It recovers a function from its gradient, and finds the area under a curve.

The rule for powers

$$\int x^n \, dx = \frac{x^{n+1}}{n+1} + c \qquad (n \neq -1)$$

Add one to the power, divide by the new power, and never forget the constant of integration $+c$ on an indefinite integral.

Worked example. $\int (6x^2 - 4x + 1)\,dx = 2x^3 - 2x^2 + x + c$