Mathematics

# Evaluate: $\displaystyle\int \dfrac { \sec ^ { 8 } x } { cosec x } d x$

##### SOLUTION
$I = \displaystyle\int \dfrac{\sec^{8}x}{cosec\,x}dx$

$I =\displaystyle \int \dfrac{\sin\,x}{\cos^{8}x}dx$

$u = \cos\,x \Rightarrow du = -\sin\,x\,dx$

$\Rightarrow I =\displaystyle \int \dfrac{-du}{u^{8}}$

$= \dfrac{u^{-7}}{7}+c$

$= \dfrac{(\cos\,x)^{-7}}{7}+c$

$= \dfrac{1}{7\cos^{7}x}+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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