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$\int cosec^6 x d x$ is equal to |
$-\cot x \frac{\cot ^5 x}{5}-\frac{2 \cot ^5 x}{3}+k$ $-\frac{\cot x}{3}+\frac{2 \cot ^5 x}{5}+2 \cot ^{-3} x+k$ $\frac{\tan ^3 x}{3}-\frac{\tan x}{5}+2 \tan ^3 x+k$ none of these |
$-\cot x \frac{\cot ^5 x}{5}-\frac{2 \cot ^5 x}{3}+k$ |
Let $I=\int cosec^6 x d x=\int cosec^4 x . cosec^2 x d x$ $=\int\left(1+\cot ^2 x\right)^2 . cosec^2 x d x=\int\left(1+\cot ^4 x+2 \cot ^2 x\right) . cosec^2 x d x$ ∴ $I=-\cot x-\frac{\cot ^5 x}{5}-\frac{2}{3} \cot ^3 x+c$ Hence (1) is the correct answer. |
