I can't remember how to integrate ye^ey with respect to y. Is it (y^2)e^xy? or do i need to do integration by parts? i just cant remember.
2 answers
oops, that was supposed to be ye^xy
Yes, you can do integration by parts. Another way is to integrate e^(xy) and then differentiate the answer w.r.t. x.
Integral of e^(x y)dy = 1/x e^(xy) + c
Differentiate both sides w.r.t. x:
Integral of ye^(x y)dy =
(y/x - 1/x^2) e^(xy) + c'
If you use this method then the integration constant is some arbitrary function of x, so when you differentiate you don't get rid of the integration constant.
Integral of e^(x y)dy = 1/x e^(xy) + c
Differentiate both sides w.r.t. x:
Integral of ye^(x y)dy =
(y/x - 1/x^2) e^(xy) + c'
If you use this method then the integration constant is some arbitrary function of x, so when you differentiate you don't get rid of the integration constant.
1 answer