`∫ (x Cos^(-1)x)/sqrt(1-x^2)`dx

Evaluate: int_((1)/(sqrt2))^(1) ((e^(cos^(-1)x))(sin^(-1)x))/(sqrt(1-x^(2)))dx

If y=(x cos^(-1)x)/(sqrt(1-x^(2)))-log sqrt(1-x^(2)), then prove that (dy)/(dx)=(co^(1-x)x)/((1-x^(2))^((3)/(2)))

Prove that (d)/(dx)(cos^(-1)x)=(1)/(sqrt(1-x^(2)) , where x in [-1,1].

If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Asqrt(1-9x^(2))+B(cos^(-1)3x)^(3)+C, then A-B is

int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k _(1)) ( sqrt(1-9x ^(2))+ (cos ^(-1) 3x )^(k_(2)))+c, then k _(1) ^(2)+k_(2)^(2)= (where C is an arbitrary constnat. )

int(1)/(cos^(-1)x.sqrt(1-x^(2)))dx=

If y=(sin^(-1)x)/(cos^(-1)x)," then "(dy)/(dx)=(k)/((cos^(-1)x)^(2)sqrt(1-x^(2)))," where "k=

int_( then )^( If )cos^(-1)x+cos^(-1)sqrt(1-x^(2))dx=Ax+f(x)sin^(-1)x-2sqrt(1-x^(2))+c

Differentiate tan^(-1)((sqrt(1-x^(2)))/(x)) wrt cos^(-1)(2x sqrt(1-x^(2))) if x varepsilon((1)/(sqrt(2)),1)