anonymous
  • anonymous
How to find this integral?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[\int\limits_{}^{} x^3 * e^{-4x^2} dx\]
anonymous
  • anonymous
I tried IBP but the integral seemed to get more complex.
anonymous
  • anonymous
Only did Integration By Parts once.

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amoodarya
  • amoodarya
\[u=-4x^2\\du=-8xdx \rightarrow xdx=\frac{ -1 }{ 8 }du\\x^3e^{-4x^2}dx=x^2*e^{-4x^2}(xdx)=\frac{-1}{4}u*e^u*(\frac{ -1 }{ 8 }du)=\\\frac{1}{32}ue^udu\] now do , integration by part
anonymous
  • anonymous
Another easy way, everytime you have an algebraic expression (like \[x^{n}\] times something
amoodarya
  • amoodarya
\[\int\limits\frac{ 1 }{ 32 }ue^udu=\frac{ 1 }{ 32 }\int\limits ue^udu=\\\]
amoodarya
  • amoodarya
can you go on , from there ?
anonymous
  • anonymous
Yes, thank you! So you have to put everything in terms of u and make the equation easier to simplify... :)

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