`intsec^(- 1)sqrt(x)dx`

Explanation

We have given `intsec^(-1)sqrtx\ dx`

`I=intsec^(-1)sqrtx\ dx`

Let `t=sqrtx implies dx=2tdt`

`I=intsec^(-1)t 2tdt`

`I=2int tsec^(-1)tdt`

By integration by parts

`I=2[(t^2)/2sec^(-1)t-int (t^2)/2.d/(dt)(sec^(-1)t)dt`

`I=2[(t^2)/2sec^(-1)t-int (t^2)/2xx1/(tsqrt(t^2-1)dt]`

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