Mathematics

# Evaluate $\int { \dfrac { \tan ^{ 7 }{ \sqrt { x } } \sec ^{ 2 }{ \sqrt { x } } }{ \sqrt { x } } } dx$

##### SOLUTION
$\int_{}^{} {\cfrac{{{{\tan }^7}\sqrt x {{\sec }^2}\sqrt x }}{{\sqrt x }}dx}$
putting $\tan \sqrt x = t$
$\Rightarrow {\sec ^2}\sqrt x \times \cfrac{1}{{2\sqrt x }}dx = dt$
$\Rightarrow \cfrac{{{{\sec }^2}\sqrt x }}{{\sqrt x }}dx = 2dt$
$= 2\int_{}^{} {{t^7}dt}$
$= 2 \times \cfrac{{{t^8}}}{8} + c$
$= \cfrac{1}{4}{\tan ^8}\sqrt x + c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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