## anonymous one year ago How to find this integral?

1. anonymous

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

2. anonymous

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

3. anonymous

Only did Integration By Parts once.

4. 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

5. anonymous

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

6. amoodarya

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

7. amoodarya

can you go on , from there ?

8. anonymous

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