Evaluate the following indefinite integral
$$\int \frac{1+x}{1+x^{2}}dx$$

Transforming it to a familiar form, we get;
$$\int \left ((1+x)\cdot \left ( \frac{1}{1+x^{2}} \right ) \right )dx$$

From here I cannot find the proper substitute to solve the problem

Question

Evaluate the following indefinite integral
$$\int \frac{1+x}{1+x^{2}}dx$$

Transforming it to a familiar form, we get;
$$\int \left ((1+x)\cdot \left ( \frac{1}{1+x^{2}} \right ) \right )dx$$

From here I cannot find the proper substitute to solve the problem

anonymous · Answer

perform integration by parts. might help you.

anonymous · Answer

I could do that, but the work is on substitution :x

nikvist · Answer

$$\int udv=uv-\int vdu\quad;\quad u=1+x\quad,\quad dv=\frac{dx}{1+x^2}$$