If `intsqrt((cosx-cos^3x)/((1-cos^3x)))dx=f(x)+c`, then f(x) is equal to

int sqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to

Evaluate: int(cos x-cos 2x)/(1-cosx)dx .

If ∫f(x) dx =Ψ(x) , then ∫x^5 f(x^3) dx is equal to

The function f(x)=(cosx+isinx)(cos3x+isin3x)...{cos(2n-1)x+isin(2n-1)x} , then f'(x) is equal to

If f(x)=cosx-cos^(2)x+cos^(3)x-…oo , then the value of int f(x) dx is equal to -

Prove : int (cos x - cos 2x)/(1-cosx) dx = x + 2 sin x + c

If inte^(sinx)[(xcos^3x-sinx)/(cos^2x)]dx=e^(sinx)*f(x)+c , where c is constant of integration, then f(x)=

If int (e^(x)(1+sinx))/(1+cos x)dx=e^(x)f(x)+c , then the value of f(x) is -

If intsqrt(cos e cx+1)dx=kfog(x)+c ,w h e r ek is a real constant, then (a) k=-2,f(x)=cot^(-1)x ,g(x)=sqrt(cos e cx-1) (b) k=-2,f(x)=tan^(-1)x ,g(x)=sqrt(cos e cx-1) (c) k=2,f(x)=tan^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1)) (d) k=2,f(x)=cot^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1))

underset(x to 0)lim((1-cos2x)(3+cosx))/(xtan4x) is equal to-