[int(1)/((2sin x+3cos x)^(2))dx= 1) (1)/(2tan x+3)+c 2) (1)/(2(2tan x+3))+c 3) -(1)/(2(2tan x+3))+c 4) -(1)/(4(2tan x+3))+c]

int(1)/(1+3cos^(2)x)dx=(1)/(2)tan^(-1)((tan x)/(2))+c

int(1)/(sin x+sqrt(3)cos x)dx=(1)/(2)log tan((x)/(2)+(pi)/(3))+c

int frac{1}{4+5 cos^2 x} dx=.............. A) (1/3) tan^(-1) ((2/3)tan x) + c B) (1/6) tan^(-1) ((2/3)tan x) + c C) (1/4) tan^(-1) ((2/3)tan x) + c D) (1/3) tan^(-1) ((1/3)tan x) + c

int(sin^(2)x)/(cos^(4)x)dx=(1)/(3)tan^(2)x+C(b)(1)/(2)tan^(2)x+C(c)(1)/(3)tan^(3)x+C(d) none

int(dx)/(4sin^(2)x+3cos^(2)x) is equal to a) (sqrt(3))/(4)tan^(-1)""((2tanx)/(sqrt(3)))+C b) (1)/(2sqrt(3))tan^(-1)""((tanx)/(sqrt(3)))+C c) (2)/(sqrt(3))tan^(-1)""((2tanx)/(sqrt(3)))+C d) (1)/(2sqrt(3))tan^(-1)""((2tanx)/(sqrt(3)))+C

If int(1)/(cos^(2)x(1-4tan^(2)x))dx=K log|(1+2tan x)/(1-2tan x)|+c, then K=

The integral int(sin^(2)x cos^(2)x)/((sin^(5)x+cos^(3)x sin^(2)x+sin^(3)x cos^(2)x+cos^(5)x)^(2))dx is equal to (1) (1)/(3(1+tan^(3)x))+C(2)(-1)/(3(1+tan^(3)x))+C(3)(1)/(1+cot^(3)x)+C(4)(-1)/(1+cot^(3)x)+C

int(1)/(7+5cos x)dx=(1)/(sqrt(6))tan^(-1)((1)/(sqrt(6))(tan x)/(2))+C(b)(1)/(sqrt(3))tan^(-1)((1)/(sqrt(3))(tan x)/(2))+C(c)(1)/(4)tan^(-1)((tan x)/(2))+C(d)(1)/(7)tan^(-1)((tan x)/(2))+C

int(sin x)/(3+4cos^(2)x)dx log(3+4cos^(2)x)+C(b)(1)/(2sqrt(3))tan^(-1)((cos x)/(sqrt(3)))+C(c)-(1)/(2sqrt(3))tan^(-1)((2backslash cos x)/(sqrt(3)))+C(d)(1)/(2sqrt(3))tan^(-1)((2backslash cos x)/(sqrt(3)))+C