" If "int(sec^(2)x-2010)/((sin x)^(2010))*dx=(P(x))/((sin x)^(2010))+C" then "P(pi/3)" is "

If int(sec^(2)x-2010)/(sin^(2010)x)dx=(P(x))/(sin^(2010) x)+C , then value of P((pi)/(3)) is

If int(sec^(2)x-2010)/(sin^(2010)x)dx=(P(x))/(sin^(2010) x)+C , then value of P((pi)/(3)) is

If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C, where f ((pi)/(4))=1, then the number of solution of the equation (f(x))/(g (x))={x} in [0,2pi] is/are: (where {.} represents fractional part function)

If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C, where f ((pi)/(4))=1, then the number of solution of the equation (f(x))/(g (x))={x} in [0,2pi] is/are: (where {.} represents fractional part function)

int_(8)^(2010)(cos^(2018)x)/(cos^(2018)x+cos(2018-x)^(2018))dx

int_(0)^( pi)xf(sin x)dx=(pi)/(2)int_(0)^( pi)f(sin x)dx

If int(sec x(2+sec x)dx)/((1+2sec x)^(2))=(sin x)/(1+cos x)+C when C is constant of ntegration then the value of P is

int_(pi//4)^(pi//3)(sec x)/(sin x)dx =

If x+i y=(-1+i sqrt(3))^(2010) , then x=