∫cosecmxcotx dx= - Infinity Learn

A
$\frac{{cosec}^{m} x}{m} + c$
B
$\frac{- 1}{m - 1} {cosec}^{m} x + c$
C
$- \frac{1}{m \sin^{m} x} + c$
D
$\frac{1}{m} \sin^{m} x + c$

Solution:

$\begin{array}{l} I = \int {cosec}^{m} x \cot x d x \\ I = \int \cos e c^{m - 1} x cosec x \cot x . d x \\ cosec x = t \\ \Rightarrow - \cos e c x . \cot x . d x = d t \end{array}$

$I = - \int t^{m - 1} . d t = \frac{- t^{m}}{m} + c$

$= - \frac{{cosec}^{m} x}{m} + c$

$= - \frac{1}{m \sin^{m} x} + c$

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$\int {cosec}^{m} x \cot x d x =$

Solution:

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