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anonymous

  • one year ago

How to find this integral?

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  1. anonymous
    • one year ago
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    \[\int\limits_{}^{} x^3 * e^{-4x^2} dx\]

  2. anonymous
    • one year ago
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    I tried IBP but the integral seemed to get more complex.

  3. anonymous
    • one year ago
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    Only did Integration By Parts once.

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

  5. anonymous
    • one year ago
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    Another easy way, everytime you have an algebraic expression (like \[x^{n}\] times something

  6. amoodarya
    • one year ago
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    \[\int\limits\frac{ 1 }{ 32 }ue^udu=\frac{ 1 }{ 32 }\int\limits ue^udu=\\\]

  7. amoodarya
    • one year ago
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    can you go on , from there ?

  8. anonymous
    • one year ago
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    Yes, thank you! So you have to put everything in terms of u and make the equation easier to simplify... :)

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