Question

Solve :
$\int \frac{1}{x(x^1+1)}dx$

Answer 1

$\int \frac{1}{\left(x\right)(x+1)}dx=\int \frac{(x+1)-\left(x\right)}{\left(x\right)(x+1)}dx$

$=\int (\frac{1}{x}-\frac{1}{x+1})dx$

$=[lnx-ln(x+1\left)\right]+C$

$=ln\left(\frac{x}{x+1}\right)+C$.