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How do you use substitution to integrate #x^3sqrt(x-3)#?

1 Answer

Jim H · mason m

Oct 15, 2015

See the explanation.

Explanation:

Let #u = x-3# so #du=dx# and #x = u+3#

Then #intx^3sqrt(x-3) dx = int (u+3)^3u^(1/2) du#

Now expand #(u+3)^3#, distribute #u^(1/2)# and finish by integrating term by term.

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