Me again, probably someone is going to blame me. I have this:
$\int{\frac{dx}{\sqrt{16-9x^2}}}$
I have asked an old teacher of mine an he said me I should let $x=\frac{4}{3}\sin{\big(\frac{3}{4}x\big)}$ but I don't how he realise that. I have tried $u-substitution$ and Integration by Parts but the square root is making the whole thing much harder. I tried multiplying both terms by $\sqrt{16-9x^2}$ but nothing. Also tried to factor to eliminate square root but nothing. I don't want that anyone solve my integral, just give me a hint about how do it, and how I can realise what to do in this cases :)