ज्ञात करें `int (1 sec^(-1) sqrtx)dx`

Explanation

`I = int sec^(-1) sqrtx dx = int (1sec^(-1)sqrtx)dx`
`=(sec^(-1)sqrtx)x-int [(1/(sqrtxsqrt(x-1))""1/(2sqrtx))x]dx`
`=x sec^(-1) sqrtx - 1/2 nit (x-1)^(-1/2) dx = x sec^(-1) sqrtx -1/2 ((x-1)^(1/2))/(1/2)+c`
` = x sec^(-1)sqrtx -1/2 (x-1)^(-1/2) dx = x sec^(-1) sqrtx = -1/2 ((x-1)^(1/2))/(1/2)+c`
`=x sec^(-1) sqrtx -(x-1)^(1/2)+c = x sec^(-1) sqrtx - sqrt(x-1) +c`