ज्ञात करें `int sin^(-1) x dx`

Explanation

`I sin^(-1) x dx = int (1sin^(-1)x) dx`
`=(sin^(-1)x)x-int(1/sqrt(1-x^2))dx = x sin^(-1)x - int x/sqrt(1-x^2)""dx`
`int x/sqrt(1-x^2)` ज्ञात करना : माना की `z=1 -x^2,` तो `dz = -2 xdx`
अब, `int x/sqrt(1-x^2)dx=int 1/sqrt2(-(dz)/2)=-1/2 intz^(-1/2)dz=-sqrtz=-sqrt(1-x^2)`
`:." "` (1) से, `I = x sin^(-1) x +sqrt(1-x^2)+c`