Question

Evaluate the following integrals:
$\int \frac{x}{1+x^2}dx$, $xϵR$

• A. $\frac{1}{3}log(1+x^3)+C$
• B. $\frac{1}{2}log(1+x^2)+C$
• C. $ta{n}^{-1}x+C$
• D. None of these
  

Answer 1

The correct option is B $\frac{1}{2}log(1+x^2)+C$

$\int \frac{x}{1+x^2}dx=\frac{1}{2}\int \frac{2xdx}{1+x^2}=\frac{1}{2}log(1+x^2)+C$