reduction formulas for n∈N, some n>0, some n>1 ∫sin^n x dx=−(1/n)cos x sin^(n−1) x +((n−1)/n)∫sin^(n−2) x dx ∫cos^n x dx=(1/n)sin x cos^(n−1) x +((n−1)/n)∫cos^(n−2) x dx ∫tan^n x dx=(1/(n−1))tan^(n−1) x −∫tan^(n−2) x dx ∫sec^n x dx=(1/(n−1))tan x sec^(n−2) x +((n−2)/(n−1))∫sec^(n−2) x dx ∫csc^n x dx=−(1/(n−1))cot x csc^(n−2) x +((n−2)/(n−1))∫csc^(n−2) x dx ∫cot^n x dx=−(1/(n−1))cot^(n−1) x −∫cot^(n−2) x dx


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Question Number 64037 by MJS last updated on 18/Nov/19

$reduction formulas for n \in N, some n > 0, some n > 1$ $\int \sin^{n} x d x = - \frac{1}{n} \cos x \sin^{n - 1} x + \frac{n - 1}{n} \int \sin^{n - 2} x d x$ $\int \cos^{n} x d x = \frac{1}{n} \sin x \cos^{n - 1} x + \frac{n - 1}{n} \int \cos^{n - 2} x d x$ $\int \tan^{n} x d x = \frac{1}{n - 1} \tan^{n - 1} x - \int \tan^{n - 2} x d x$ $\int \sec^{n} x d x = \frac{1}{n - 1} \tan x \sec^{n - 2} x + \frac{n - 2}{n - 1} \int \sec^{n - 2} x d x$ $\int \csc^{n} x d x = - \frac{1}{n - 1} \cot x \csc^{n - 2} x + \frac{n - 2}{n - 1} \int \csc^{n - 2} x d x$ $\int \cot^{n} x d x = - \frac{1}{n - 1} \cot^{n - 1} x - \int \cot^{n - 2} x d x$
Commented byRio Michael last updated on 12/Jul/19

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