Antiderivatives

Vocabulary flashcards covering common indefinite integral rules and properties.

Power Rule for Indefinite Integrals ($\int x^n\,dx$)

$\frac{x^{n+1}}{n+1} + C$ (where $n \neq -1$)

Integral of ($\int \frac{1}{x}\,dx$)

$$\ln|x| + C$$

Integral of ($\int e^x\,dx$)

$$e^x + C$$

Integral of ($\int \sin(x)\,dx$)

$$-\cos(x) + C$$

Integral of ($\int \cos(x)\,dx$)

$$\sin(x) + C$$

Integral of ($\int \sec(x)\tan(x)\,dx$)

$$\sec(x) + C$$

Integral of ($\int \sec^2(x)\,dx$)

$$\tan(x) + C$$

Integral of ($\int \tan(x)\,dx$)

$$\ln|\sec(x)| + C$$

Integral of ($\int \frac{1}{\sqrt{1 - x^2}}\,dx$)

$$\arcsin(x) + C$$

Integral of ($\int \frac{1}{1 + x^2}\,dx$)

$$\arctan(x) + C$$