" 6) "quad f(3sin x cos^(2)n-sin^(3)n)*dx

int x^(2)sin^(n)x^(3)cos x^(3)dx

If quad f_(n)(x)=(sin x)/(cos3x)+(sin3x)/(cos3^(2)x)+(sin3^(2)x)/(cos3^(3)x)+....+(sin3^(n-1)x)/(cos3^(n)x) then f_(2)((pi)/(4))+f_(3)((pi)/(4))=

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

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)

If a cos^(3)x+3a cos x sin^(2)x=m and a sin^(3)x+3a cos^(2)x sin x=n, then prove that (m+n)^((2)/(3))+(m-n)^((2)/(3))=2a^((2)/(3))

The value of the integral int_0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n) x)dx is :

(i) int sin^2x cos^3x dx (ii) int sin^3 x cos^2 x dx (iii) int sin^3 x cos^3 x dx

int(3cos3x-2sin2x)/(cos2x+sin3x)dx

If f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=

If f(x) = (cos x + i sin x)(cos 3x + i sin 3x) ….(cos (2n - 1)x + i(sin(2n - 1)x) , then f^(11)(x) is