Evaluate `sin^(-1)((x+sqrt(1-x^2))/(sqrt2))`, where `-1/sqrt2ltxlt1/sqrt2`

Evaluate int(1)/((x+1)sqrt(x^(2)-1))dx

Evaluate int(1)/(x^(2)sqrt(1+x^(2)))dx .

Evaluate int 1/(sqrt (x^2+2x+2))dx

If y = sin ^(-1) (2x sqrt (1- x ^(2))), - (1)/( sqrt2) le x le (1)/( sqrt2) , then (dy)/(dx) is equal to a) (x)/( sqrt (1- x ^(2))) b) (1)/( sqrt(1- x ^(2))) c) (2)/( sqrt (1 - x ^(2))) d) (2x)/( sqrt (1- x ^(2)))

Consider the function f(x)=sin^(-1)(2xsqrt(1-x^2)),(-1)/sqrt2lexle1/sqrt2 Find f'(x) .

Consider the function f(x)=sin^(-1)(2xsqrt(1-x^2)),(-1)/sqrt2lexle1/sqrt2 Show that f(x)=2sin^-1x

Differentiate sin^(-1) ( 2 x sqrt( 1 - x^(2))) with respect to x if (1)/( sqrt(2)) lt x lt 1

Differentiate sin^(-1) ( 2 x sqrt( 1 - x^(2))) with respect to x if - (1)/( sqrt(2)) lt x lt (1)/( sqrt(2))

Find dy/dx of y=sin^-1 2xsqrt(1-x^2) (-1)/sqrt2 < x <1/sqrt2