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(1)/(x^((2)/(3))sqrt(x^((2)/(3))-4))...

`(1)/(x^((2)/(3))sqrt(x^((2)/(3))-4))`

Text Solution

Verified by Experts

`"Let I"=int (1)/(x^((2)/(3))sqrt(x^((2)/(3)-4)))dx`
`=int (x^((-2)/(3)))/(sqrt(x^((1)/(3)-4)))dx`
`"Put" x^((1)/(3))=t therefore (1)/(3)x^((-2)/(3))dx=dt therefore x^((-2)/(3))dx=3.dt`
`therefore I=int (1)/(sqrt(t^(2)-4)).3dt=3 int (1)/(sqrt(t^(2)-4))dt`
`=3 log|t+sqrt(t^(2)-4)+c`
`=3log|x^((1)/(3))+sqrt(x^((2)/(3))-4)|+c`
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