Mathematics

# Solve:$\int {\frac{{dx}}{{x + {x^{ - 3}}}}}$

##### SOLUTION
$I=\displaystyle\int \dfrac{dx}{x+x^{-3}}$
$=\displaystyle\int \dfrac{x^3dx}{x^4+1}$
Let $x^4+1=t$
$4x^3dx=dt$
$x^3dx=\dfrac{1}{4}dt$
$\Rightarrow I=\dfrac{1}{4}\displaystyle\int \dfrac{dt}{t}$
$=\dfrac{1}{4}ln|t|+c$
$=\dfrac{1}{4}ln|1+x^4|+c$.

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

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