Question

Evaluate: ∫ dx/1 + e^x 

Answer 1

∫ dx/1 + e^x = ∫ e^–x/(e^–x + 1) dx 

Let e^–x + 1 = t 

– e^–x dx = dt 

= – ∫ dt/ t + 1 

= – log |t + 1| + c 

= – log |e ^–x + 1| + c