`int(sin x)/(cos^(3)x(1+cos^(8)x)^(3/4))*dx=f(x)*(1+cos^(8)x)^((1)/(lambda))+c` Then `lambda*f((pi)/(3))=`

int(sin^(8)x-cos^(8)x)/(1-2sin^(2)x cos^(2)x)dx=

If intsqrt((cos x-cos^(3)x)/(1-cos^(3)x))dx=f(x)+c , then f(x)=

Let int (cos x dx)/(sin^3 x (1 + sin^6 x))^(2/3) = f(x), (1 + sin^6 x )^(1/lambda) + C then find the value of lambda f(pi/3)

int_(0)^((pi)/(4))(sin x)/(cos3x+3cos x)dx

(sin x)/(sin x)=lambda cos(x)/(8)-cos(x)/(4)cos(x)/(2), then lambda =

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)

int_(0)^( pi)sin^(3)x(1+2cos x)(1+cos x)^(2)dx

if sin x+sin^(2)x=1 then cos^(12)x+3cos^(10)x+3cos^(8)x+cos^(6)x=

int(1)/(4cos x+3sin x)dx