Mathematics

# Solve:$\dfrac{1}{2}\int {\dfrac{{{u^2}}}{{1 + u}}du}$

##### SOLUTION
$I =\dfrac {1}{2} \int\dfrac {u^2 du}{1+u}$

$=\dfrac {1}{2}\int \dfrac {(u^2-1+1)du}{1+u}$

$=\dfrac {1}{2}\int \dfrac {(u^2-1)}{1+u}du +\dfrac {1}{2}\int \dfrac {1}{1+u}du$

$=\dfrac {1}{2}\int \dfrac {(u+1)(u-1)}{(u+1)}du \,\, \dfrac {1}{2} \int \dfrac {1}{u+1}du$

$=\dfrac {1}{2}\left [ \dfrac{u^2}{2}-u \right ]+\dfrac {1}{2}log |u+1| +C$

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

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