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:

if x^(2) !=npi+1 , ninN then int x sqrt((2sin(x^(2)-1)-sin2(x^(2)-1))/(2sin(x^(2)-1)+sin2(x^(2)-1))) dx is equal to (a) In cos ((x^(2)-1)/(2))+c (b) (1)/(2)In cos ((x^(2)-1)/(2))+c (c) In sec ((x^(2)-1)/(2))+c (d) (1)/(2)In sec ((x^(2)-1)/(2))+c

For x^2nenpi+1, n inN (the set of natural numbers), the integral intxsqrt((2sin(x^2-1)-sin2(x^2-1))/(2sin(x^2-1)+sin2(x^2-1))) dx is equal to (where c is a constant of integration)

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

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_(0)^(pi)(sin(n+1/2)x)/(sin(x/2))dx is

For n in N , the value of int_(0)^(pi) sin^(n) x*cos^(2n-1)x dx is

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

The value of the integral int_0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n) x)dx is :

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