Evaluate the indefinite integral: y^3*sqrt(y + 5) dy.

Answer 1

again let u = (y+5)
then du = dy
and y = u-5
y^3 = u^3-15u^2+75u-125

and integral of
(u^3-15u^2+75u-125)u^(1/2) du
or
u^(7/2) du - 15 u^(5/2)du + 75 u^(3/2) du - 125 u^(1/2) du
which is (2/9)u^(9/2) ..... etc