Posted by **CMM** on Thursday, January 27, 2011 at 11:15pm.

Evaluate the indefinite integral. Please check my work? Not sure if I am doing this correctly.

S= integral symbol

S x^3*sqrt(x^2 + 1) dx

u = x^2+1

x^2= u - 1

du = 2xdx

du/2 = xdx

1/2 S x^2 * x sqrt (x^2 + 1) du

1/2 S (u - 1) * sqrt (u) du multiply square root of u and (u - 1)

FOIL (u - 1) * sqrt (u)

=((u)^3/2) - ((u)^1/2)

= 1/2 S (((u)^3/2) - ((u)^1/2)) du Now take the derivative and keep the 1/2 on the side.

1/2 ((u)^5/2)/(5/2) - ((u)^3/2)/(3/2) now distribute the 1/2 and bring the 5/2 and 3/2 to the top

1/2 * 2/5 * (u)^5/2 - 1/2 * 2/3 * (u)^ 3/2

cut all the 2 and substitute x^2+1 in the place of u.

so the final answer is

1/5 (x^2 - 1)^5/2 - 1/3(x^2 - 1)^3/2

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