Question Number 21076 by j.masanja06@gmail.com last updated on 11/Sep/17
$${integrate}\:{with}\:{respect}\:{to}\:{x} \\ $$$$\int{x}^{{sinx}} \\ $$
Answered by FilupS last updated on 17/Sep/17
$$\int{x}^{\mathrm{sin}\left({x}\right)} {dx}=\int{e}^{\mathrm{sin}\left({x}\right)\mathrm{ln}\left({x}\right)} {dx} \\ $$$$=\int\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}^{{n}} \left({x}\right)\mathrm{ln}^{{n}} \left({x}\right)}{{n}!}{dx} \\ $$$$=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}!}\int\mathrm{sin}^{{n}} \left({x}\right)\mathrm{ln}^{{n}} \left({x}\right){dx} \\ $$$$=??? \\ $$