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How do you find the integral of #(x^3)((x^2 + 4)^(1/2)) dx#?

1 Answer

Oct 10, 2015

Let #u=x^2+4#.

Explanation:

#int x^3(x^2 + 4)^(1/2) dx = intx^2(x^2+4)^(1/2)xdx#

Let #u=x^2+4#, so that #du=2xdx# and #x^2=u-4#.

After substitution, the integral becomes:

#1/2 int (u-4)u^(1/2)du#

Distribute the #u^(1/2)# and finish the integral.

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