Question

Can I use the Tabular Method to do this integral?: Integrate (x^3)(e^(x^2)dx

Answer 1

Hmm this one is a little tricky.
I think we want to make a `U substitution` before we try integrating.\[\huge \int\limits\limits\limits x^3 e^{(x^2)}\;dx \qquad = \qquad \int\limits\limits\limits \color{royalblue}{x^2} e^{(\color{royalblue}{x^2})}(\color{orangered}{x\;dx})\]

Answer 2

\[\large \color{royalblue}{u=x^2}\]Taking the derivative of our substitution, with respect to x gives us,\[\large \frac{du}{dx}=2x \qquad \rightarrow \qquad du=2x \;dx\]Divide both sides by 2, giving us,\[\large \color{orangered}{\frac{1}{2}du=x\;dx}\]

Plug the orange and blue in,

Answer 3

\[\huge \int\limits \color{royalblue}{u} e^{(\color{royalblue}{u})}\left(\color{orangered}{\frac{1}{2}du}\right)\]

Answer 4

Integrating either by tabular method or otherwise, will be a lot easier from this point.

You can probably do tabular method right from the start somehow, but I wasn't able to figure it out myself :C

Answer 5

Yeah, I think you've got me headed in the right direction. I wasn't even thinking to pull an 'x' out to make two x^2s...I should be able to get it from here, the e^(x^2) was really throwing me off. Appreciate the help, and that's awesome how you were able to type is out like that :D

Answer 6

hehe yah, the colors make it a little clearer :) I like that.

Answer 7

I don't think you can use Tabular at the start because of that e^(x^2)...does that even have an anti-derivative?

Answer 8

You could do this maybe, lemme try real quick...

Answer 9

I keep getting stuck here, because I don't know how to do the tabular method :) lol
I generally do `by parts` the normal way.