How do you integrate ((x)√x−1)dx?
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★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 }
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