Hi

Can someone tell me where my mistake is for the following questions:

1)Evaluate the integral $\displaystyle \frac{e^{x}}{1+e^{2x}}$

$\displaystyle u = e^{x}$

$\displaystyle u' = e^{x}$

$\displaystyle dx = \frac{du}{e^{x}}$

$\displaystyle \frac{e^{x}}{1+e^{2x}} * \frac{du}{e^{x}}$

$\displaystyle e^{x}$ cancels so i get:

$\displaystyle \frac{1}{1+e^{2x}} + C$

Not sure if this is correct?

2)Evaluate the integral $\displaystyle \sqrt{1 + \sqrt{x}}$

This is what i have done:

$\displaystyle u = \sqrt{x}$

$\displaystyle u' = \frac{1}{2}x^{-0.5}$

$\displaystyle dx = \frac{du}{\frac{1}{2}x^{-0.5}}$

final answer i got was $\displaystyle \frac{4}{3}x^{\frac{3}{2}} + x^2 + C$

P.S