Mathematical formulas

Calculus II

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Formula · Mathematical formulas

5.3. Typical reduction formulas

Formula

Formula

\int csc^{n} x d x = - \frac{csc ^{n - 2} x cot x}{n - 1} + \frac{n - 2}{n - 1} \int csc^{n - 2} x d x, n > 1

Variables

\int sec^{n} x d x = \frac{sec ^{n - 2} x tan x}{n - 1} + \frac{n - 2}{n - 1} \int sec^{n - 2} x d x, n > 1

\int cot^{n} x d x = - \frac{cot ^{n - 1} x}{n - 1} - \int cot^{n - 2} x d x, n > 1

\int tan^{n} x d x = \frac{tan ^{n - 1} x}{n - 1} - \int tan^{n - 2} x d x, n > 1

\int cos^{n} x d x = \frac{cos ^{n - 1} x sin x}{n} + \frac{n - 1}{n} \int cos^{n - 2} x d x, n \geq 2

\int sin^{n} x d x = - \frac{sin ^{n - 1} x cos x}{n} + \frac{n - 1}{n} \int sin^{n - 2} x d x, n \geq 2

\int x^{n} e^{a x} d x = \frac{x ^{n} e ^{a x}}{a} - \frac{n}{a} \int x^{n - 1} e^{a x} d x, a \neq = 0