It's difficult to judge the difficulty from appearance. sqrt(tan x) may look simple but it's more tedious to integrate than some horrible looking functions.why does Sharkys Integral look much easier compared to that
One more question
(It can be solved without knowing the result in #217.)
Continuing from aboveI have decided to give up @sharky564 question.
This is a new question that should be solvable in 4U.
That last section which results in a dilogarithm is entirely 4U-able, and you may see that if you try the Feynman in a slightly different way.
Let's try Feynman trick.
(Let t=cos x)
Note that I(0)=0 and let
This will unfortunately lead to dilogarithm but at least this is a way out. I will be extremely impressed if someone can provide a solution using 4U methods.
Yes, it is a good idea (unless you want to use trig identities many times or prove a reduction formula first)Let t=tanx is a good idea?
I guess you must have got an answer close to zero.Let t=tanx is a good idea?
With the usual trick, f(x)+f(pi/2-x)=-cos(2x) ln(tan x), which can be evaluated by IBP.This one is fun
HSC is over but a good integral is always fun:This one is absolutely painful.
I have skipped the steps of rationalization.The algebra is quite annoying.