Question

integral of e^x(sqrt(1+e^(2x)))dx

Answer 1

∫ e^x √(1+e^(2x)) dx

Note that if u = e^x, you have

∫ u√(1+u^2) du

Now, if v = 1+u^2, dv = 2u du, and you have

1/2 ∫ √v dv

That I think you can handle, eh?

Answer 2

wouldn't it be the integral of sqrt(1+u^2)du instead of integral u(sqrt (1+u^2)du because the du takes care of the outside u?

Answer 3

you are correct. My bad. Good catch.