`int(sin^(3)x cos^(5)x-cos^(3)x sin^(5)x)ln(sin2x)*dx=f(x),` where `f((pi)/(4))=-(1)/(256)` then the value of `f((5 pi)/(4))` equals

f (x) = ln (sin x) ^ (2) then f ((pi) / (4)) =

f(x)=int x^(sin x)(1+x cos x*ln x+sin x)dx and f((pi)/(2))=(pi^(2))/(4) Then the value of |cos(f(pi))| is

if int(1-5sin^(2)x)/(cos^(5)x sin^(2)x)dx=(f(x))/(cos^(5)x)+c then f(x)

If F(x)=int(x+sin x)/(1+cos x)dx and F(0)=0 then the value of f((pi)/(2)) is

if int e^(sin x)(x cos^(3)x-sin x)/(cos^(2)x)dx and f(0)=1 then f(pi)= is

Let f(sin x)=(1-sin^(5)x)^((1)/(5)) then what is the value of f(f(cos x))

For x in(0, (pi)/(2)) If int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c and f((pi)/(3))=(3)/(2) then [f((pi)/(4))] = ( where [.] denotes G.I.F )

For x in [0, (pi)/(2)] if int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c and f((pi)/(3))=(3)/(2) then f((pi)/(4)) = (where[.] denotes I F)

Let (d)/(dx)(f(x))=((sin^(12)x-cos^(12)x)/((sin^(2)x-cos^(2)x)(1-3sin^(2)x cos^(2)x))) be such that f(0)=0 then f((pi)/(2)) equals (k pi)/(16). Find the value of k(k in N)