How does integration by parts work?

In summary, integration by parts is a method of integration that is used when the integrand can be written in the form of u(x) * dv/dx. This method involves using the product rule of differentiation in reverse to simplify the integral. The steps involved include choosing u(x) and dv/dx, applying the product rule, and then integrating the resulting equation. If needed, this process may need to be repeated multiple times until the integral can be solved. Other methods, such as substitution, can also be used to solve integrals.
  • #36
help with integration by parts *urgent*

i need help with this because it's driving me crazy.
I need to integrate:

X^3(e^(3x^2))

I can do simpler integration by parts but i can't get this one to work out. The answer works out to:

[(x^2)/6 -1/18]e^(3x^2) please be very detailed, because I know how to do simpler integration by parts, but this example is proving to be very difficult.
 
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  • #37
Put this into a separate post
 

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