Mathematics

# Evaluate : $\int \dfrac{x^4+1}{x^2+1}dx$.

##### SOLUTION
Given $\int {\dfrac{x^4+1}{x^2+1}dx}$
$=\int {\left(\dfrac{2}{x^2+1}+x^2-1\right)dx}$
$=2\int{\dfrac{1}{x^2+1}dx}+\int{x^2 dx}-\int{1dx}$
$=2(\tan^{-1}x)+\dfrac{x^3}{3}-x+C$
$=2\tan^{-1}x+\dfrac{x^3}{3}-x+C$

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

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