How do I solve for the integration of x^2 e^(x^3) without a prefix?

[rugapark]

intergrating "e"

I'm doing some intergration q's and I'm stuck on one which involves e


[x^2 e^(x^3) ]dx


I know to integrate you "add one to the power and divide by the new power.. would that make the solution

((x^3)/3) ((e^(x^4))/(x^4)? hope that makes a bit of sense..

 

[2slowtogofast]

try u substition

 

[nicksauce]

Nope it doesn't really make sense

First,
$$\int f(x)g(x)dx\neq \int f(x)dx \int g(x)dx$$
Second,
$$\int e^{x^n}dx \neq \frac{e^{x^{n+1}}}{x^{n+1}}$$

That sort of rule only works for the forms x^n and not anything else. The "only" way to integrate an exponential, is to use $$\int e^xdx = e^x$$. In this case, you can't do that directly, but a substituion u = x^3 should do the trick.

 

[rugapark]

great - cheers for that i get it now :)