Mathematics

# $\displaystyle \int{ { e }^{ 3\log { x } }{ \left( { x }^{ 4 }+1 \right) }^{ -1 }dx }$ is equal to ?

##### ANSWER

$\dfrac { 1 }{ 4 } \log { \left( { x }^{ 4 }+1 \right) } +C$

##### SOLUTION
$\int e^{3 \log x} (x^{4}+1)^{-1} dx= \int e^{\log x^{3}} (x^{2}+1)^{-1} dx$
$= \int \dfrac{x^{3}}{1+x^{4}} dx$
Let $14x^{4} =t$
$x^{3} dx =dt$
$\Rightarrow = \int \dfrac{dt}{4t}$
$=\dfrac{1}{4} \log t+c$
$=\dfrac{1}{4} \log (1+x^{4})+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
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