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)`

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

int_ (lambda =) (dx) / (sqrt (1-tan ^ (2) x)) = (1) / (lambda) sin ^ (- 1) (lambda sin x) + C, then

" Let " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}| then find the values of f(0) and f' (pi//2) .

If f(x)=lambda|sin x|+lambda^(2)|cos x|+g(lambda) has a period =(pi)/(2) then find the value of lambda

int_(, then f(x))^( If )(dx)/(x^(3)(1+x^(6))^(2/3))=x*f(x)*(1+x^(6))^(1/3)+C

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

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 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))=

If f(x)=x+sin x, then find the value of int_(pi)^(2 pi)f^(-1)(x)dx

"Let f(x) "=|{:(cos x" " sin x" " cos x),(cos 2x" "sin 2x" "2cos 2x),(cos 3x" "sin 3x" "3cos 3x):}|" Then find the vlue of "f'(0) and f'(pi//2).