Integrate (e^(ax+by))(a*cos(xy)-y*sin(xy)) dx?

Question

idealist10 · Answer

I want to type this in Equation so you can see better but I can't. Sorry. But please help me with this problem.

demonchild99 · Answer

holy crap wat grade u in

hartnn · Answer

thats not as difficult as it seems

demonchild99 · Answer

lucky...i never been to good at math

hartnn · Answer

y is constant for that integral

idealist10 · Answer

I know that y is constant since it's dx at the end so I pulled put e^(by) with a.

hartnn · Answer

note this down :
$\Large \int e^{x}[f(x)+f'(x)] = e^x f(x)+c$

hartnn · Answer

your integral is of that form

hartnn · Answer

derivative of cos(xy) is -y sin(xy)

idealist10 · Answer

I know that the answer is cos(xy)(e^(ax+by)) but I don't know how to get e^(ax+by) in the answer. I know that I need to treat e^(by) as constant but why does the answer include e^(ax)?

hartnn · Answer

that would be a shortcut
if you need to show your work

integration by parts
twice
for both terms
separately

hartnn · Answer

$\int e^{ax} \cos bx$
and
$\int e^{ax} \sin bx$
formulas

idealist10 · Answer

Nah~, I did that but it's TOO much work, it only complicated the problem more. And I don't need to show work for this problem.

hartnn · Answer

using those direct formulas is too muck work ??
i anticipate that there will be dew terms getting cancelled...but just a guess (didn't solve it on paper)

hartnn · Answer

**few terms

idealist10 · Answer

How did you get cos bx and sin bx?

hartnn · Answer

thats just general form

hartnn · Answer

a e^(ax) cos (xy)

hartnn · Answer

and
-y e^(ax) sin (xy)

and entire thing multiplied by e^(by)

hartnn · Answer

$\Large a\int  e^{ax} cos (xy)dx$
hard ?

idealist10 · Answer

No.

hartnn · Answer

$\Large -y\int  e^{ax} \sin (xy)dx$

its called breaking a complex problem into easier smaller pieces.
we do that a lot in programming :P

idealist10 · Answer

I get it now. Thank you so much for the help! Do you know how to program?

hartnn · Answer

i do programming for a living :)

hartnn · Answer

in C language as of now, but learning others

idealist10 · Answer

I have a question. Is website a software?

hartnn · Answer

software is a very general term

since you write codes to make a software and a website too, you can say , in a way, yes

idealist10 · Answer

Thank you!

hartnn · Answer

^_^