Question

How to find this integral?

Answer 1

\[\int\limits_{}^{} x^3 * e^{-4x^2} dx\]

Answer 2

I tried IBP but the integral seemed to get more complex.

Answer 3

Only did Integration By Parts once.

Answer 4

\[u=-4x^2\\du=-8xdx \rightarrow xdx=\frac{ -1 }{ 8 }du\\x^3e^{-4x^2}dx=x^2*e^{-4x^2}(xdx)=\frac{-1}{4}u*e^u*(\frac{ -1 }{ 8 }du)=\\\frac{1}{32}ue^udu\]
now do , integration by part

Answer 5

Another easy way, everytime you have an algebraic expression (like \[x^{n}\] times something

Answer 6

\[\int\limits\frac{ 1 }{ 32 }ue^udu=\frac{ 1 }{ 32 }\int\limits ue^udu=\\\]

Answer 7

can you go on , from there ?

Answer 8

Yes, thank you! So you have to put everything in terms of u and make the equation easier to simplify... :)