Question Number 1000 by rpatle69@gmail.com last updated on 13/May/15

∫e^(x  ) sinx dx=?  plz give me answer soon.

Commented byrpatle69@gmail.com last updated on 13/May/15

please soon guys

Answered by prakash jain last updated on 13/May/15

I=∫e^x sin xdx  Integrate by parts  I=e^x (−cos x)+∫e^x cos xdx  Integrate e^x cos x by parts  =−e^x cos x+e^x sin x−∫e^x sin xdx  =−e^x cos x+e^x sin x−I  2I=e^x sin x−e^x cos x  I=(1/2)(e^x sin x−e^x cos x)+C  (d/dx)[(1/2)(e^x sin x−e^x cos x)+C]  =(1/2)[e^x sin x+e^x cos x−e^x cos x+e^x sin x]  =e^x sin x

Commented byrpatle69@gmail.com last updated on 13/May/15

thanks