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Evaluate: int1/((x+3)sqrt(x-1))\ dx...

Evaluate: `int1/((x+3)sqrt(x-1))\ dx`

Text Solution

Verified by Experts

Let `I=int(1)/((x-3)sqrt(x+1))dx`
`" Let " x+1=t^(2) " or " dx=2t dt`
`:. I=int(1)/((t^(2)-1-3))(2t)/(sqrt(t^(2)))dt`
`=2int(dt)/(t^(2)-2^(2))=2xx(1)/(2(2))log|(t-2)/(t+2)|+C`
`=(1)/(2)log|(sqrt(x+1)-2)/(sqrt(x+1)+2)|+C`
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