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 Q1   Integrate the functions  \frac{2x}{1+ x ^2}

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Given to integrate \frac{2x}{1+ x ^2} function,

Let us assume 1+x^2 =t

we get, 2xdx = dt

\implies \int \frac{2x}{1+x^2} dx = \int \frac{1}{t} dt

= \log|t| +C

= \log|1+x^2| +C    now back substituting the value of t = 1+x^2

as (1+x^2) is positive we can write 

= \log(1+x^2) +C

Posted by

Divya Prakash Singh

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