Integral from Pi/4 to Pi/3 of ln(tanx)dx/sinxcosx
I know 2sinxcosx = sin2x, but does this even help? Derivative of tanx = sec^2x = 1/cos^2x but I don't think this helps either. Any help/advice?
Thanks!
Hello Sprintz!
First use a variable substitution: $\displaystyle u=\log\tan(x) \Rightarrow du=\frac{1}{\sin(x)\cos(x)}dx$
Then insert back into the integral and cancel out and get (mind the changed integration boundaries): $\displaystyle \int_0^{\log\sqrt{3}}udu=\frac{u^2}{2}\big|_0^{\lo g\sqrt{3}}=\frac{1}{2}(\log\sqrt{3})^2$
Hmm kind of embarrassing that I couldn't get that eh? Is it a matter of simply memorizing these derivatives and integrals? I have a test tomorrow (hence the review problems) and will have to know all of them.
Any tips to do so? My memory is really lacking. Is it a matter of doing the same types of problem enough to gain familiarity?
I've exhausted all of the problems in my textbook. Does anyone know if there is a website that generates Integral problems, or a list somewhere of problems that I can look over? I find this to be the most efficient method of review.
Cheers