Antiderivatives and Indefinite Integrals

Antiderivatives

Definition

$F$ is an antiderivative of $f$ if $F'(x) = f(x)$.

Basic rules

• $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ (for $n \neq -1$)
• $\int e^x dx = e^x + C$
• $\int \frac{1}{x} dx = \ln|x| + C$
• $\int \sin x \, dx = -\cos x + C$
• $\int \cos x \, dx = \sin x + C$