Integration by Parts for Complex Integrals

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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)
 
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donglepuss said:
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.
 
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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.
 
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It looks like you are trying to use integration by parts repeatedly, which should work if you do it right. As a reminder:
$$\int udv = uv - \int vdu$$
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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