Mathematics

# Evaluate: $\int x \sec ^ { 2 } x d x$

##### SOLUTION
$I=\int x\sec^2xdx$

We know that
$\int uv =u\int v-\int (\int v)\dfrac{du}{dx}.dx$

$u=x$   $v=\sec ^2x$

$I=x\int \sec ^2x-\int (\int \sec ^2x).1dx$

$I=x\tan x-\int \tan xdx$

$I=x\tan x-\ln |\sec x|+c$.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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