i need the integral of:
e^ax * cos(bx) *dx
x^k * sin(ax) *dx
x^k * e^ax *dx
thanks in advance
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
We know that (from the product rule) so choose:
Now do .
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 :
(Oops! As Soroban, Krizalid, and Jhevon all said, you need to add an arbitrary constant to this. Wow was I slow on this one! )
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?