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Evaluate: int1/(x^(3)sqrt(x^2-1))\ dx...

Evaluate: `int1/(x^(3)sqrt(x^2-1))\ dx`

Text Solution

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Let, `x=sec theta`
`dx=sec theta tan theta d theta`

`=int1/(x^(3)sqrt(x^2-1))\ dx`

`=int1/(sec^3 theta sqrt(sec^2 theta-1))\ sec theta tan theta d theta`

`=int1/(sec^2 theta tan theta)\ tan theta d theta`

`=int1/(sec^2 theta)\ d theta`

`=int cos^2 theta d theta`

`=int (1+cos2 theta)(2) d theta`
...
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