this is part of an integration, thats why i posted it here.

the needed substitution here is

i end up with this sometime, which is correct:

2\sqrt{sin(x)}-\frac{2*\sqrt{(sin(x))^5}}{5}+C

Mr F says: You mean }" alt="{\color{red}

2\sqrt{sin(x)}-\frac{2*\sqrt{(sin(x))^5}}{5}+CMr F says: You mean }" />

.
now my book says the result should be:

and wofram alpha says it should be:

to be honest... i tried and i tried, i dont get it how i will get any of those 2 solutions. would be so nice if someone could explain it me reeeeal slow

thx in advance