So I'm still a beginner with integrating by substituting.
What I know is that you use 'u' from one of the thing in the equation to substitute.
Though, I'm not entirely sure where 'u' should be coming from.
So I did u = (1-x2)
And since it has a cube root, I did this:
1/3 du = 3√(1-x2)dx
So I got: ∫1/3 u1/3 du
4/3 u4/3 + C -> 4/3 (1-x2)3 + C
But I'm not sure if this is entirely correct after:
Someone else showed me how to do the steps, which was this:
∫5x 3√(1-x2)dx = -5/2∫(1-x2)1/3(-2x)dx = -5/2 * ((1-x2)4/3)/(4/3) + C = (-15/8) * (1-x2)4/3 + C
This was the correct answer in the book.
But I'm a bit confused on how the person got the -5/2, and the (-2x)
Can someone explain to me that part?