Help with integrals?

Question

I need help with these two equations, please help

integral from 5 to 1 of (x/ square root of (2x -1)) dx


and

integral ((x^(2) - 1) / square root of (2x - 1)) dx

Answer 1

Are you familiar with the method of Substitution?

I would use u=2x-1, which means x=(u+1)/2 and du=2dx (so dx=du/2).

The first one becomes
int (u+1)/(4 Sqrt u) du
= (1/4) int [u^.5 + u^(-.5)] du
etc.

The point is, the substitution moves the complicated stuff out from under the radical sign, so you can work with it.

Same sub should work with second problem, too.

Last remark, if you see an integral sign with a 1 at the bottom and a 5 at the top, that's "Integral from 1 to 5...". The given problem might have been what you said, but I think this order of integration is more common.