Mathematics

# Evaluate $\displaystyle \int \dfrac{3x^{2}}{x^{6}+1}dx$

##### SOLUTION

Consider the given integral.

$I=\int{\dfrac{3{{x}^{2}}}{{{x}^{6}}+1}}dx$

$I=\int{\dfrac{3{{x}^{2}}}{{{\left( {{x}^{3}} \right)}^{2}}+1}}dx$

Let $t={{x}^{3}}$

$dt=3{{x}^{2}}dx$

Therefore,

$I=\int{\dfrac{dt}{{{t}^{2}}+1}}$

$I={{\tan }^{-1}}t+C$

On putting the value of $t$, we get

$I={{\tan }^{-1}}\left( {{x}^{3}} \right)+C$

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

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