Mathematics

Evaluate:  $\displaystyle\int \dfrac{(1+x+x^2)dx}{x(1+x^2)}$.

$lnx + tan^{-1}x + C$

SOLUTION
$\displaystyle \int \dfrac {(1+x+x^2)}{x(1+x^2)}dx$
$=\displaystyle \int \dfrac {(1+x^2)}{x(1+x^2)}dx+\displaystyle \int \dfrac {x}{x(1+x^2)}dx$
$=\displaystyle \int \dfrac {1}{x}dx +\displaystyle \int \dfrac {1}{1+x^2}dx$
$\ln (x)+\tan^{-1} (x)+C$

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

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