Question

How to integrate e^x^2 * x^3?

Answer 1

This?\[
\int \exp(x^2)x^3\;dx
\]

Answer 2

\[
\int \exp(x^2)x^3\;dx=\int \exp(x^2)x^2\;(xdx)
\]Let \(u=x^2,du=2xdx\)\[
\frac{1}{2}\int ue^u\;du
\]

Answer 3

\(\exp(x)=e^x\)

Answer 4

And x to the power of 2.

Answer 5

\[
\exp(x^2)=e^{x^2}
\]

Answer 6

Yes,that's it.

Answer 7

\[
\exp(x^2)x^3=e^{x^2}x^3
\]See? It's the same thing dude.

Answer 8

Oh sorry.But I don't learn like that before.

Answer 9

It's better not to make towers \[\large
e^{x^{x^{e^{x^{x}}}}}
\]

Answer 10

Okay.

Answer 11

But how about x^3?

Answer 12

∫exp(x2)x3dx=∫exp(x2)x2(xdx)
Let u=x2,du=2xdx
12∫ueudu
So if there is 2∫exp(x2)x3dx this will become 2*12∫ueudu, right?