`(cosx)/((1-sinx)(2-sinx))` [Hint : Put sin x = t]

Integrate the functions 1/(xsqrt(ax-x^(2))) [Hint: Put x = a/t ]

Integrate the rational functions 1/((e^(x)-1)) [Hint : Put e^(x) = t]

int(sin2x)/((sinx+cosx)^2)dx

Let f(x)=((2sinx+sin2x)/(2cosx+sin2x)*(1-cosx)/(1-sinx)): x in R. Consider the following statements. I. Domain of f is R. II. Range of f is R. III. Domain of f is R-(4n-1)pi/2, n in I. IV. Domain of f is R-(4n+1)pi/2, n in I. Which of the following is correct?

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

int(dx)/(cosx-sinx)=...+c

The number of distinct real roots of |{:(sinx,cosx,cosx),(cosx,sinx,cosx),(cosx,cosx,sinx):}|=0 in the interval -pi/4lexlepi/4 is "........."

If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+\ ddotto\ oo)))) , prove that (dy)/(dx)=((1+y)cosx+ysinx)/(1+2y+cosx-sinx)

Integrate the rational functions in exercise. (cosx)/((1-sinx)(2sinx))