Integration by Parts for Complex Integrals

[donglepuss]

Homework Statement

integral of x^12 sinx dx

Relevant Equations

answer: x^12 -cosx - 12x^11 sinx - cosx (132x^11/11)

integral of x^12 sinx dx = x^12 -cosx - 12x^11 sinx - cosx (132x^11/11)

 

[Mark44]

Homework Statement: integral of x^12 sinx dx
Homework Equations: answer: x^12 -cosx - 12x^11 sinx - cosx (132x^11/11)

integral of x^12 sinx dx = x^12 -cosx - 12x^11 sinx - cosx (132x^11/11)

No, it's not.
However, you should get into the habit of checking your work when you have an integration problem. Just differentiate your answer, and if it is correct, you'll end up with the original integrand.

 

[Eclair_de_XII]

Might I suggest trying to use recurrence relations? I'm not sure if it's the best idea, though.

In any case, what I did was set $I(n)=\int x^n \sin(x) \ dx$ where $n$ is a positive integer.

 

[tnich]

It looks like you are trying to use integration by parts repeatedly, which should work if you do it right. As a reminder:
$$\int udv = uv - \int vdu$$