Mathematics

# $\displaystyle \int \frac{d\left ( x^{2}+1 \right )}{\sqrt{x^{2}+2}}$ is equal to

$\displaystyle 2\sqrt{x^{2}+2}+k$

##### SOLUTION
$\displaystyle \int \frac{d\left ( x^{2}+1 \right )}{\sqrt{x^{2}+2}}$

$\displaystyle I=\int \frac { 2x }{ \sqrt { x^{ 2 }+2 } } dx$

Put $x^{ 2 }+2=t$
$\Rightarrow 2xdx=dt$

$\displaystyle I=\int \frac { 1 }{ \sqrt { t } } dt$
$\Rightarrow \displaystyle I=2\sqrt{t}+k$
$I=2\sqrt { x^{ 2 }+2 } +k$

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

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