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Evaluate: int1/(x^(2setminus3)sqrt(x^(2s...

Evaluate: `int1/(x^(2setminus3)sqrt(x^(2setminus3)-4))\ dx`

Text Solution

Verified by Experts

I=`int1/(x^(2setminus3)sqrt(x^(2setminus3)-4))\ dx`
let `(x^(2setminus3)-4=t^2`
`(dx)/(x^(1/3))=3tdt`
So,
`I=int (dt)/(x^(1/3)x^(1/3)sqrt(x^(2/3)−4))`
`I=int (3tdt)/(sqrt(t^2) sqrt(t^2+4))`
`I=int (3tdt)/(tsqrt(t^2+4))`
`I=3int (dt)/(sqrt(t^2+4))`
...
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