Question

How do you evaluate the indefinite in integral? Use C for constant integration

`int(2+4x)/(1+x^2)dx`

Answer 1

`int (2+4x)/(1+x^2) dx = 2arctanx + 2ln(1+x^2) +C`

Explanation:

Using the linearity of the integral:

`int (2+4x)/(1+x^2) dx = 2int dx/(1+x^2) + 2 int (2xdx)/(1+x^2)`

`int (2+4x)/(1+x^2) dx = 2arctanx + 2 int (d(1+x^2))/(1+x^2)`

`int (2+4x)/(1+x^2) dx = 2arctanx + 2ln(1+x^2) +C`