Question

Use substitution to solve:
int_{0}^{ln(sqrt{3})}(e^x/(1+e ^{2x}))dx

Answer 1

\[\int\limits_{0}^{\ln(\sqrt3)}(e^x/(1+e^{2x}))dx\]

Answer 2

let u = e^(x) so du = e^x*dx
then change your limits
bottom limit is e^0 = 1
top limit is ln(e^(√3)) = √3
the integrand should simplify to du/(1+x^2) which is the arctan. Then evaluate at the endpoints and subtract.

Answer 3

why is the top limit sqrt(3)? shouldent it be e^(ln(sqrt3))

Answer 4

well i guess that is the same thing so nvm lol ty