" fisint "(x-(x^(2))/(2)+(x^(3))/(4)cdots cdots)+cos^(-1)(x^(2)-(x^(4))/(2)+(x^(6))/(4)cdots cdots oo)=(pi)/(2)" for "0<|x|

If sin^(-1)(x-(x^(2))/2+(x^(3))/4-……oo) +cos^(-1)(x^(2)-(x^(4))/2+(x^(6))/4-……..oo)=(pi)/2 and 0ltxltsqrt(2) then x=

intx cdot root(3)(x+2)dx

intx^(2) cdot 10^(x^(3))dx

e^((x-1)-(1)/(2)(x-1)^(2)+((x-1)^(3))/(3)-((x-1)^(4))/(4)+...cdots) is eqaul to

int e^((1)/(x))cdot(1)/(x^(2))dx

intx^(2) cdot root(3)(x^(3)+8)dx

y=((x+1)^(2)cdot sqrt(x-1))/((x+3)^(3)e^(x))

int_(-pi)^(pi) (1 - x^2)sin x cdot cos^2 x cdot dx is :

y=((x+1)^(2)cdot sqrt(x-1))/((x+3)^(3)e^(x)) Find dy/dx

If x + y + z = xyz, then prove that (2x)/(1- x^(2)) + (2y)/(1 - y^(2)) + (2z)/(1 - z^(2)) = (2x)/(1 - x^(2))cdot (2y)/(1 - y^(2))cdot (2z)/( 1- z^(2)) .