Calculus Integration Formulas and Trigonometric Identities

Flashcards covering standard indefinite integrals of exponential, logarithmic, trigonometric, and inverse trigonometric functions, as well as trigonometric double-angle identities.

$$\int \frac{du}{u}$$

$$\ln|u| + C$$

$$\int e^u\,du$$

$$e^u + C$$

$$\int a^u\,du$$

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

$$\int \sin(u)\,du$$

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

$$\int \cos(u)\,du$$

$$\sin(u) + C$$

$$\int \sec^2(u)\,du$$

$$\tan(u) + C$$

$$\int \csc^2(u)\,du$$

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

$$\int \sec(u)\tan(u)\,du$$

$$\sec(u) + C$$

$$\int \csc(u)\cot(u)\,du$$

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

$$\int \cot(u)\,du$$

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

$$\int \sec(u)\,du$$

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

$$\int \csc(u)\,du$$

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

$$\int \frac{du}{\sqrt{a^2 - u^2}}$$

$$\arcsin\left(\frac{u}{a}\right) + C$$

$$\int \frac{du}{a^2 + u^2}$$

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

$$\int \frac{du}{u\sqrt{u^2 - a^2}}$$

$$\frac{1}{a}\operatorname{arcsec}\left(\frac{|u|}{a}\right) + C$$

$$\sin(2\theta)$$

$$2\sin(\theta)\cos(\theta)$$

$$\cos(2\theta)$$

$$\cos^2(\theta) - \sin^2(\theta) = 2\cos^2(\theta) - 1 = 1 - 2\sin^2(\theta)$$