The integral $\int \frac{2 x+x^3}{1+x^2} dx$ is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$ where C is a constant of integration
$\int \frac{2 x+x^3}{1+x^2} dx$
$=\int\frac{x^3+x}{x^2+1}+\frac{x}{x^2+1}dx$
$=\int x+\frac{1}{2}\frac{2x}{(x^2+1)}dx$
$=\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$