Question

Evaluate:

`∫ e^x/(1 + e^(2x))dx`

Answer 1

Given:

`∫ e^x/(1 + e^(2x))dx`

Let e^x = t

e^x dx = dt

I = ∫ `dt/(1 + t^2)`

I = tan⁻¹ t + C

I = tan⁻¹ (e^x) + C

∫ `e^x/(1 + e^2x)dx = tan^(−1) e^x + C`