1. ## Integration by parts

hi, i was wondering if i did a certain problem right.

i have to integrate the following by parts:

x * the square root of x-1

i set u = x, u' = 1, v' = (x-1)^(1/2) and v = 2/3(x-1)^(1/2)

then from there i got:

x * 2/3(x-1)^(1/2) times the integral of 2/3(x-1)^(1/2)

i integrated the 2/3(x-1)^(1/2) and got 4/9(x-1)^(3/2)

then, i multiplied it by the x * 2/3(x-1)^(1/2).

for a final answer, i got:

x * 2/3(x-1)^(1/2) * 4/9(x-1)^(3/2)

is this right or am i missing something?

2. Heir