Mathematics

# $2 \int \dfrac{tdt}{t^4+1}=\dfrac{1}{\sqrt{m}}tan^{-1}{t^2}$.Find the value of $m$

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##### SOLUTION
$2\int { \dfrac { t\;dt }{ { t }^{ 4 }+1 } }$
Let $t^2=M$
$\Rightarrow 2+dt=dM$       ( On differentiating w.r.t $t$ )
$\Rightarrow \dfrac { 2 }{ 2 } \int { \dfrac { dM }{ { M }^{ 2 }+1 } =\tan ^{ -1 }{ M } +C }$
$=\tan^{-1}\left(t^2\right) +C.$
Hence, the answer is $\tan^{-1}\left(t^2\right) +C.$

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

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