Integrating Powers of x (Edexcel A-Level Mathematics): Flashcards

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

$\int x^{-1} dx = \ln|x| + C$

When $n = -1$, because it causes division by zero.

$\int x^2 dx = \frac{x^3}{3} + C$

$\int x^{-3} dx = -\frac{1}{2x^2} + C$, for $x \neq 0$

Evaluate the antiderivative at limits and subtract.

$\int_a^b x^n dx = \frac{x^{n+1}}{n+1}\bigg|_a^b$

$C$ is the constant of integration.

$\int \text{expression} \, dx$, where $dx$ is the variable.

$\int(5x^{1/2} + 2) dx = \frac{10}{3}x^{3/2} + 2x + C$