Integral ((e^x)*(1-(e^2x))^1/2 dx
How can I solve this one. I don't know how to start it.
Thank you
$\displaystyle \int \sqrt{e^x(1-e^{2x})} \delta x$
I'm still learning this myself, but I'm fairly sure that you would do this using substitution. I'm not suggesting that this is the best way to solve it, but note how using $\displaystyle z=e^x$ alters the question:
$\displaystyle \int \sqrt{z (1-2z)} \delta x$
$\displaystyle \int \sqrt{z - 2z^2} \delta x$
Perhaps you'll be able to solve it from here?
are you sure you don't mean $\displaystyle \int e^x \sqrt{1 - e^{2x}}~dx$ ?
if that is the case, begin with a substitution of $\displaystyle u = e^x$. this yields the integral
$\displaystyle \int \sqrt{1 - u^2}~du$
the conventional way to deal with this latter integral is to use trig substitution, that is, substitute $\displaystyle u = \sin \theta$
If $\displaystyle e^x = z,$ then $\displaystyle e^{2x} = z^2$.
I suggest you combine the terms and then take $\displaystyle e^{2x}$ as a common factor and take it out. Then use a substitution that will get rid of the $\displaystyle e^x$ outside, and use another (trigonometric) substitution to solve. This way isn't pretty and I'm trying to find another easier way.
EDIT: @Jhevon: he did pepper it with parentheses, so I don't think there is an ambiguity here: the $\displaystyle e^x$ is in the square root.
EDIT2: See ya!