Question

Integrate the function: $\frac{2x}{1+x^2}$

Answer 1

Let 1+x2 = t

∴ 2x dx = dt

$\Rightarrow \int \frac{2x}{1+x^2}dx=\int\frac{1}{dt}$

= log |t| +C
= log |1+x2| +C
= log (1+x2) +C