# integration by part

• February 27th 2008, 09:51 AM
ramzouzy
integration by part
hi..
im struggling to get the right answer by integrating this function here by parts:

integral[2e^(-1/2t)*sin(3t)dt]

the answer seems to be -(24/37)e^(-t/2)*cos(3t)-(4/37)e^(-1/2t)*sin(3t)+c

id appreciate all the steps with it since i want to see where ive gone wrong

thanks
• February 27th 2008, 03:01 PM
CaptainBlack
Quote:

Originally Posted by ramzouzy
hi..
im struggling to get the right answer by integrating this function here by parts:

integral[2e^(-1/2t)*sin(3t)dt]

the answer seems to be -(24/37)e^(-t/2)*cos(3t)-(4/37)e^(-1/2t)*sin(3t)+c

id appreciate all the steps with it since i want to see where ive gone wrong

thanks

Put:

$I=\int 2 e^{-t/2} \sin(3t)~dt$

Integrate by parts, then do so again and you will have a load of stuff plus a
multiple of the original integral on the right hand side (which we are calling $I$).
Now solve the equation for $I$.

RonL