Mathematics

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


ANSWER

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


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
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