# partial integral of e^xy

• Jun 25th 2010, 03:25 PM
isuckatcalc
partial integral of e^xy
not sure if that title makes sense...

here's the problem i need to solve
find the integral of: (ye^xy)dx

so since i'm integrating with respect to x, i first just tack on an x, to get:

xye^xy. right?

now i need to divide by the derivative of xy, since e^xy. this is where i'm stuck. since i'm integrating only with x, does that mean i take the partial derivative of xy with respect to x? leaving me with just y.

so then i'd end up with xe^xy. is that the right answer?
• Jun 25th 2010, 03:33 PM
mr fantastic
Quote:

Originally Posted by isuckatcalc
not sure if that title makes sense...

here's the problem i need to solve
find the integral of: (ye^xy)dx

so since i'm integrating with respect to x, i first just tack on an x, to get:

xye^xy. right?

now i need to divide by the derivative of xy, since e^xy. this is where i'm stuck. since i'm integrating only with x, does that mean i take the partial derivative of xy with respect to x? leaving me with just y.

so then i'd end up with xe^xy. is that the right answer?

I assume you can integrate something like $2 e^{2x}$ .... ? Or even $k e^{kx}$ ....? This is no different. y is treated as a constant. The required integral is $e^{yx}$. Differentiate this result to see if it's still unclear.
• Jun 25th 2010, 03:49 PM
isuckatcalc
this is my third attempt to reply... odd problems

the derivative of e^xy is (e^xy)/y. correct?

so that'd cancel out the y in the numerator and leave me with xe^xy, as i originally thought. i'm still not sure that's the right answer though.
• Jun 25th 2010, 03:55 PM
isuckatcalc
nevermind, i got it now. thanks for the help
• Jun 25th 2010, 03:56 PM
mr fantastic
Quote:

Originally Posted by isuckatcalc
this is my third attempt to reply... odd problems

the derivative of e^xy is (e^xy)/y. correct?

so that'd cancel out the y in the numerator and leave me with xe^xy, as i originally thought. i'm still not sure that's the right answer though.

No! Do you know how to differentiate $e^{2x}$? Have you been taught a formula for differentiating $e^{kx}$?

If y is treated as a constant and x is the variable then the derivative of $e^{yx}$ is $y e^{yx}$.
• Jun 25th 2010, 04:02 PM
isuckatcalc
yeah, i was completely overthinking the problem. thanks for your help, i did get it, unfortunately not until after i made my first reply to the post.