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int 1/(xsqrt(x^4-1))dx...

`int 1/(xsqrt(x^4-1))dx`

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The correct Answer is:
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Let ` I= int(dx)/(xsqrt(x^(4)-1))`
Put `x^(2) = sec theta rArr theta = sec^(-1)x^(2)`
`rArr 2x dx = sec theta. tan theta d theta`
`I = 1/2 int(sec theta. tan theta)/(sec theta tan theta) d theta = 1/2 int d theta = 1/2 theta + C`
`= 1/2 sec^(-1)(x^(-2)) + C`
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