how do I solve integral xe^x^2 -x

Question

anonymous · Answer

$$\int\limits xe^{x^2} - x dx = \frac{1}{2}(e^{x^2}+x^2)$$

anonymous · Answer

You can see by using the fact that integration is the opposite of integration. Oops missed the constant of integration off the end...

anonymous · Answer

opposite of differentiation*

anonymous · Answer

Thanks for your effort, but i'm guessing you didn't just 'see' that answer? Is there a specific method you can use to solve this integral?

anonymous · Answer

Firstly I notice that $$xe^{x^2}$$ isn't a standard thing. Recall that the chain rule for differentiation says that if we have a function of a function, we differentiate the inside function and then the outside one. We know that when we differentiate the x^2 we get 2x so $$\frac{d}{dx}e^{x^2}=2xe^{x^2}$$
That's nearly what we've got, just two times it. So we want half of what we tried. 

Hope that makes more sense.

anonymous · Answer

Yes it does. Thanks