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

integrate using chain rule

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!

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

You need to apply integration by parts three times here!

@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?

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

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

oh what answar said!

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.

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

good now right?

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

i think that should be a positive 6x

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