∫e^x/(e^{2x} + 1)dx = ?

Question

\(\int\frac{e^x}{(e^{2x}+1)}dx\) = ?

∫e^x/(e^2x + 1)dx

A. cot^-1(e^x) + c

B.tan^-1(e^x) + c

C.2tan^-1(e^x) + c

D. none of these

Answer 1

= \(\int\frac{e^x}{(e^x)^2+1^2}dx\)

e^x = t 

e^x dx = dt

put t = e^x 

tan^-1 e^x + c