How to integrate complicated differential equation

[trojansc82]

Homework Statement

I need to integrate ∫ -y³e^y2/2

Homework Equations

Integration by parts

The Attempt at a Solution

I have tried several times, I am unable to find the correct solution, which is:

-ye^y2/2 + 2e^y2/2 + c

 

[shelovesmath]

Homework Statement

I need to integrate ∫ -y³e^y2/2

Homework Equations

Integration by parts

The Attempt at a Solution

I have tried several times, I am unable to find the correct solution, which is:

-ye^y2/2 + 2e^y2/2 + c

I think you can use u substitution. Let u = y^2, du = 2y. If you factor that y^3 at y^2 * y it should work. You might have to also do integration by parts afterwards.

 

[Samuelb88]

Try a u-substitution.

 

[hunt_mat]

Here is a possibly slicker method, calculate:
$$\int ye^{ay^{2}}dy$$
This should be very straight forward, the result should be a function of a, all you do now is differentiate the result with respect to a and then set a=1/2.