If `int(3cot3x-cotx)/(tanx-3tan3x)dx = pf(x) + qg(x)+C`, then which of the following may be correct?

If int (3cot 3 x-cot x)/(tanx-3tan3x)dx=pf(x)+qg(x)+C , where C is a constant of integration, then

int(cot x+cot^(3)x)/(1+cot^(3)x)dx

tan^(3)x-3tanx=0

inte^x(cotx-1-cot^2 x)dx=

Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos 3x+sin3x-sin x)/(2(sin 2x+cos2x)))^(2) . Then, which of the following is (are) correct ?

int(sec^2x)/(sqrt(2tan^2x+3tanx+3))dx=

int(3cotx - 2 tanx)^(2) dx

int(2tanx)/(2+3tan^(2)x)dx=

If int(cos 4x+1)/(cotx-tanx)dx=a cos 4x+c, then a=