## Calculus 10th Edition

The required formula is $$\int \frac{1}{z}dz=\ln |z|+c.$$
The integral $$\int \frac{x}{x^2+1}dx$$ can be transformed into integral $$\frac{1}{2}\int \frac{1}{z}dz$$ using substitution $z=x^2+1,$ where is $dz=2xdx$ so required formula is $$\int \frac{1}{z}dz=\ln |z|+c.$$