Table of Indefinite Integrals and Antiderivatives

Flashcards covering standard integration formulas and antiderivatives for common functions, including polynomials, exponentials, trigonometric, and inverse trigonometric expressions.

Antiderivative of $k$

$kx + C$ (Formula: $\int k\,dx = kx + C$)

Antiderivative of $x^n$ ($n \neq -1$)

$\frac{x^{n+1}}{n+1} + C$ (Formula: $\int x^n\,dx = \frac{x^{n+1}}{n+1} + C$)

Antiderivative of $e^{kx}$

$\frac{1}{k}e^{kx} + C$ (Formula: $\int e^{kx}\,dx = \frac{1}{k}e^{kx} + C$)

Antiderivative of $a^{kx}$

$\frac{a^{kx}}{k\ln(a)} + C$ (Formula: $\int a^{kx}\,dx = \frac{a^{kx}}{k\ln(a)} + C$)

Antiderivative of 1/x

$\ln(|x|) + C$ (Formula: $\int \frac{1}{x}\,dx = \ln(|x|) + C$)

Antiderivative of $\cos(kx)$

$\frac{1}{k}\sin(kx) + C$ (Formula: $\int \cos(kx)\,dx = \frac{1}{k}\sin(kx) + C$)

Antiderivative of $\sin(kx)$

$-\frac{1}{k}\cos(kx) + C$ (Formula: $\int \sin(kx)\,dx = -\frac{1}{k}\cos(kx) + C$)

Antiderivative of $\sec^2(kx)$

$\frac{1}{k}\tan(kx) + C$ (Formula: $\int \sec^2(kx)\,dx = \frac{1}{k}\tan(kx) + C$)

Antiderivative of $\sec(kx)\tan(kx)$

$\frac{1}{k}\sec(kx) + C$ (Formula: $\int \sec(kx)\tan(kx)\,dx = \frac{1}{k}\sec(kx) + C$)

Antiderivative of 1/1-(kx)²

$\frac{1}{k}\arcsin(kx) + C$ (Formula: $\int \frac{1}{\sqrt{1-(kx)^2}}\,dx = \frac{1}{k}\arcsin(kx) + C$)

Antiderivative of 1/1+(kx)²

$\frac{1}{k}\arctan(kx) + C$ (Formula: $\int \frac{1}{1+(kx)^2}\,dx = \frac{1}{k}\arctan(kx) + C$)