When to use Integral Substitution? $e^x$$(1+e^x)^{1\over{2}}$
why can't use integration by part, 
What is meant by in the form of f(g(x))g'(x)?
Can you give a few example?
Thank you

in your example i would set $t=\sqrt{1+e^{x}}$ then we get $t^2=1+e^{x}$ and we have $2tdt=e^xdx$ thus your integral is $2\int t^2dt$
