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I really need help in evaluating this integral

Evaluate the integral

integrate of (dx)/((e^x)+e^(2x))

change of variables

let u = e^-x

du/dx = -e^-x

dx = -e^x du

dx = -u^-1 du

S(dx)/((e^x)+e^(2x)) =

S (-u^-1)du / (u^-1 + u^-2) =

-S du/(1+u^-1) =

-S udu/(u+1) =

-S (1 - 1/(u+1)) du =

S (1/(u+1) - 1) du =

ln(u+1) - u

since u = e^-x , we now have

S(dx)/((e^x)+e^(2x)) = ln(e^-x + 1) - e^-x

The answer is ln(e^-x + 1) - e^-x

Calculus

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I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

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