If `x^2!=n pi-1, n in N`. Then, the value of `int x sqrt((2sin(x^2+1)-sin2(x^2+1))/(2sin(x^2+1)+sin2(x^2+1)))dx` is equal to:

For x ^ 2 ne n pi + 1, n in N ( the set of natural numbers ), the integral int x sqrt ((2 sin (x ^ 2 - 1 ) - sin 2 (x ^ 2 - 1 ))/(2 sin ( x ^ 2 - 1 ) + sin2 (x ^ 2 - 1 ) )) dx is

The value of int _(-1)^(1) (x)/(sqrt(1-x^(2))). sin^(-1) (2xsqrt(1-x^(2)))dx is equal to

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

The integral int((sin2x+cos^(2)x)dx)/(1+sin^(2)x(sin2x-cos^(2)x)) is equal to

int_(-1)^(1)(x)/(sqrt(1-x^(2)))*sin^(-1)(2x sqrt(1-x^(2)))dx is equal to

int_0^(pi//2) (sin^(1//2)x)/(sin^(1//2)x+cos^(1//2)x) dx is equal to

int(1)/(1+sin2x+sin^(2)x)dx=

The value of int _(0)^(pi//2) ((sin x + cos x)^(2))/(sqrt(1+sin 2x) dx is