Table of Standard Integrals

Vocabulary flashcards covering the standard indefinite integration formulas from the reference table.

$$\int x^n \, dx$$

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

$$\int \frac{dx}{x}$$

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

$$\int e^x \, dx$$

$$e^x + C$$

$$\int a^x \, dx$$

$$\frac{a^x}{\ln(a)} + C$$

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

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

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

$$\sin(x) + C$$

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

$$\tan(x) + C$$

$$\int \csc^2(x) \, dx$$

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

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

$$\sec(x) + C$$

$$\int \csc(x) \cot(x) \, dx$$

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

$$\int \frac{dx}{1+x^2}$$

$$\arctan(x) + C$$

$$\int \frac{dx}{\sqrt{1-x^2}}$$

$$\arcsin(x) + C$$

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

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

$$\int \cot(x) \, dx$$

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

$$\int \sec(x) \, dx$$

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

$$\int \csc(x) \, dx$$

$$-\ln(|\csc(x) + \cot(x)|) + C$$

$$\int \frac{dx}{a^2 + x^2}$$

$$\frac{1}{a} \arctan\left(\frac{x}{a}\right) + C$$

$$\int \frac{dx}{\sqrt{a^2 - x^2}}$$

$$\arcsin\left(\frac{x}{a}\right) + C \quad (a > 0)$$