Is there any reduction formula possible?

Question

$$ I=\int_{0}^ {\pi} e^{x} (sinx)^{n} dx $$. I tried a lot but unable to obtain and stuck by it.

Maybe you wouldn’t mind sharing what you tried, so that people don’t keep repeating your errors? — DonielF, Aug 14 '17 at 14:39

hamam_Abdallah · Answer 1 · 2017-08-14T21:43:02.013

4

hint

integrate by parts twice to find a recursive formula between $I_n $ and $I_{n-2} $.

$$I_n=-n\int_0^\pi \sin^{n-1}(x)\cos (x)e^xdx $$ $$=n \int_0^\pi \Bigl((n-1)(\sin^{n-2}(x)-\sin^n (x))-\sin^n (x)\Bigr)e^xdx $$

edited Aug 14 '17 at 21:43

answered Aug 14 '17 at 12:43

hamam_Abdallah

Should i first integrate it twice, by parys method . – Girish Kumar Chandora Aug 14 '17 at 12:45
@GirishKumarChandora Yes. $u=sin^n v'=e^x$ – hamam_Abdallah Aug 14 '17 at 12:49
thnks a lot for giving hint. Now i did it. – Girish Kumar Chandora Aug 14 '17 at 12:50
@GirishKumarChandora If that helped, there’s a check mark you can hit to indicate that as the correct answer for your purposes. – DonielF Aug 14 '17 at 14:40

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