Integrating exponential functions

[Pingunoot]

How would you integrate something like xe(x^2) by using a substitution like u=x^2

 

[CompuChip]

What is du?

 

[Pingunoot]

2x, but my problem is how will this help when you still have e raised to the power u

 

[elibj123]

Do you know what's

$$\int e^{u}du$$

?

 

[Pingunoot]

Do you know what's

$$\int e^{u}du$$

?

no this is what I am stuck on

 

[elibj123]

Well, you know that integration is some sort of anti-derivative, and you know that a function of which derivative is e^x, is e^x it self. So it's safe to say that:

$$\int e^{u}du=e^{u}+C$$

 

[Pingunoot]

Well, you know that integration is some sort of anti-derivative, and you know that a function of which derivative is e^x, is e^x it self. So it's safe to say that:

$$\int e^{u}du=e^{u}+C$$

Thanks for your help, that cleared things up.

 

[Anonymous217]

just to clarify, du is 2x(dx), not just not 2x. I'm sure you already knew that though.