Mathematical formulas

Calculus II

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Formula · Mathematical formulas

A.2. Trigonometric integrals

Formula

Formula

\int tan^{n} u d u = \frac{1}{n - 1} tan^{n - 1} u - \int tan^{n - 2} u d u

Variables

\int cos^{n} u d u = \frac{1}{n} cos^{n - 1} u sin u + \frac{n - 1}{n} \int cos^{n - 2} u d u

\int sin^{n} u d u = - \frac{1}{n} sin^{n - 1} u cos u + \frac{n - 1}{n} \int sin^{n - 2} u d u

\int csc^{3} u d u = - \frac{1}{2} csc u cot u + \frac{1}{2} ln ∣ csc u - cot u ∣ + C

\int sec^{3} u d u = \frac{1}{2} sec u tan u + \frac{1}{2} ln ∣ sec u + tan u ∣ + C

\int cot^{3} u d u = - \frac{1}{2} cot^{2} u - ln ∣ sin u ∣ + C

\int tan^{3} u d u = \frac{1}{2} tan^{2} u + ln ∣ cos u ∣ + C

\int cos^{3} u d u = \frac{1}{3} (2 + cos^{2} u) sin u + C

\int sin^{3} u d u = - \frac{1}{3} (2 + sin^{2} u) cos u + C