Question

How do you integrate ((x)√x−1)dx?

Answer 1

★GOOD MORNING★

Integration of x √(x - 1 ) dx

put x - 1 = z²

DIFFERENTIATE BOTH SIDE'S W.R.T x

dx = 2z dz

=>

Integration of 2 ( z² × ( z² + 1 ) dz

=>

Integration of 2 ( z⁴ + z² ) dz

=>

2 { z^5 /5 + z³/3 )

=>

2 { ( √x-1)^1/5 + ( √x-1 )³ /3 }

Answer 2

please see the attachment