First, I apologize for the lack of LaTeX. I do not have the compiler installed on this machine.
The problem I am stuck on asks me to integrate x^3 * sqrt(1-x^2), with u=1-x^2.
To begin, I set u=1-x^2, du = -2x. I also restructured the original problem as follows: x^2 * sqrt(1-x^2) * x
With substitution, this gave me: -1/2 [Integral] (1-u)*sqrt(u) du
However, it all goes downhill from there, and I'm unable to reach what I know to be the correct answer, as provided to me by the professor: -1/15(1 - x^2) ^ 3/2 * (2 + 3x^2)
Any help on where I'm going wrong is greatly appreciated.
The problem I am stuck on asks me to integrate x^3 * sqrt(1-x^2), with u=1-x^2.
To begin, I set u=1-x^2, du = -2x. I also restructured the original problem as follows: x^2 * sqrt(1-x^2) * x
With substitution, this gave me: -1/2 [Integral] (1-u)*sqrt(u) du
However, it all goes downhill from there, and I'm unable to reach what I know to be the correct answer, as provided to me by the professor: -1/15(1 - x^2) ^ 3/2 * (2 + 3x^2)
Any help on where I'm going wrong is greatly appreciated.
