HI ,
i need the integral of:
e^ax * cos(bx) *dx
x^k * sin(ax) *dx
x^k * e^ax *dx
thanks in advance
Assume , the solution is trivial in any of the cases a = 0 or b = 0 or both a = b = 0.
So, if we can proceed by Integration by parts.
.......do this last integral by parts again
Someone please check this. I still get lost when typing out solutions with LaTex
I see others replying to the thread, so i'll hold off on answering the others. i'd only answer one though, since the last two are kind of similar
Look up integration by parts. The first one is the trickiest so I'll do that one.
We know that (from the product rule) so choose:
==>
==>
So:
Now do .
Choose
==>
==>
Then
Now substitute this value for the sin(bx) integral into your cos(bx) expression:
This would apparently give us nothing because the solution of the integral depends on the value of the integral! But treat as a variable for the moment. If we add to both sides...
Now factor the common :
-Dan
(Oops! As Soroban, Krizalid, and Jhevon all said, you need to add an arbitrary constant to this. Wow was I slow on this one! )
By the way!!!
Soroban, did you add me to your msn list?
I already added you. My msn is asymmetrical_line@hotmail.com
I hope to see you there!!
the second one is a bit more complicated i believe. we have to deal with factorials and also, i think, we have to do two cases: if k is odd or even. don't think we need cases for the third, but factorials may come into play again
it seems everyone else simplified their answer. turns out i was the lazy one here...hey, i had to leave something for fid to do on this question, right?