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

Answer 1

Cameron Alexander

See the 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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Answer 2

Paisley Johnson

To integrate (x^3\sqrt{x-3}) using substitution, we can let (u = x - 3). Then, (du = dx). The integral becomes (\int (u + 3)^3\sqrt{u} , du). Now, we can expand ((u + 3)^3) using binomial expansion, and then integrate the resulting expression.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.