Integrate x^3*e^x^3 dx
--Integration by parts is what section it's in.

Question

anonymous · Answer

integrate using chain rule

anonymous · Answer

if i factor out an x and get x*x^2(e^x^3) then i think I can integrate using the parts.
Ill let you know when i get an answer and you can tell me if its right!

anonymous · Answer

$$\int\limits_{}^{}x^{3}e ^{x^{3}} dx$$
$$=e ^{x^{3}}\int\limits_{}{}x^3dx + x^3\int\limits_{}^{}e ^{x ^{3}}dx$$

anonymous · Answer

You need to apply integration by parts three times here!

anonymous · Answer

@AnwarA: Can you help me out with what the first parts are?
If i want to get it in the form of $$uv- \int\limits\limits vdu$$
then what would my first u and dv be?

anonymous · Answer

you are trying to do a u - sub and parts at the same time, i don't think it is going to work.  you just have to grind it out.  you should make the "u" be x^3, then x^2, then x, because the exponent decreases every time, and of course e^x stays the same

anonymous · Answer

but my main problem is just integrating e^x^3

anonymous · Answer

oh what answar said!

anonymous · Answer

OH WOW I FAIL.   So sorry guys but i wrote the problem down wrong.  The REAL question is $$\int\limits x ^{3}e ^{x ^{}}dx$$
Where it is much simpler to do integration by parts a second time.

anonymous · Answer

i was just going to ask for what the actual problem was.

anonymous · Answer

good now right?

anonymous · Answer

yup!  I had to integrate by parts THREE times (really, seems a bit dramatic) but I got
$$e ^{x}(x ^{3}-3x ^{2}-6x-6) + C$$
which is cool because in that polynomial you can actually see the full derivative simplification of x^3

myininaya · Answer

i think that should be a positive 6x