Math help please, x(Sqrt[13-x^2] I need to integrate this
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Math help please, x(Sqrt[13-x^2] I need to integrate this

[From: ] [author: ] [Date: 11-05-14] [Hit: ]
......
So I need to integrate x(Sqrt[13-x^2]

I understand that the answer is -1/3 (13-x^2)^3/2

I just don't understand the steps involved to solve it.

-
∫ [x][sqrt(13 - x^2)] dx

Let u = 13 - x^2
du = -2x dx
dx = -1/(2x) du

Sub that back in and that x's will cancel, leaving the -1/2 to be factored out:

(-1/2) ∫ sqrt(u) du
(-1/2) ∫ u^(1/2) du
(-1/2)(2/3)u^(3/2)
(-1/3)u^(3/2)
(-1/3)[13 - x^2]^(3/2) + C

Done!
1
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