`∫sqrt(x) sin^(2)(x^(3/2)-1)dx`

Evaluate: ( i ) int(1+sin x)/(sqrt(x-cos x))dx (ii) int(1)/(sqrt(1-x^(2))(sin^(-1)x)^(2))dx

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

Find:int_(0)^((1)/(sqrt(2)))(sin^(-1)x)/((1-x^(2))^((3)/(2)))dx

int_(0)^(1//sqrt(2))(sin^(-1)x)/((1-x^(2))^(3//2))dx=?

(int(sin^(3/2)x+cos^(3/2)x)dx)/(sqrt(sin^(3)x cos^(3)x sin(x-alpha)))

I_(1)=int_(1)^(2)sqrt(sin(3x-x^(2)-2))dx and I_(2)=int_(1)^(3)sqrt(sin((4x-x^(2)-3)/(4)))dx then the value of 2I_(1)-I_(2) is

If I=int(x cos x+1)/(sqrt(2x^(3)e^(sin x)+x^(2)))dx=(A)/(9)log|(sqrt(2xe^(sin x)+1)-1)/(sqrt(2xe^(sin x)+1)+1)|+C, then A is equal to

If int(sin x)/(sin^(2)x+4cos^(2)x)dx=(1)/(sqrt(3))Tan^(-1)((g(x))/(sqrt(3)))+c then g(x)=.....

int_(0)^(1)sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))dx

int(sin^(2)x*sec^(2)x+2tan x*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx