Mathematics

# Evaluate: $\int { \dfrac { { x }^{ 2 }dx }{ ({ x }^{ 2 }+1)({ x }^{ 2 }+2) } }$

$\sqrt { 2 } \tan ^{ -1 }{ \frac { x }{ \sqrt { 2 } } -\tan ^{ -1 }{ x } +c }$

##### SOLUTION
Given,

$\int \dfrac{x^2}{\left(x^2+1\right)\left(x^2+2\right)}dx$

using partial fraction, we get,

$=\int \dfrac{2}{x^2+2}-\dfrac{1}{x^2+1}dx$

$=\int \dfrac{2}{x^2+2}dx-\int \dfrac{1}{x^2+1}dx$

$=\sqrt{2}\tan ^{-1}\left(\dfrac{x}{\sqrt{2}}\right)-\tan ^{-1}\left(x\right)+C$

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

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