`int tan^(-1) ((sin2x)/(1+cos 2x))dx`

Evaluate the following integrals: int tan^(-1)((sin2x)/(1+cos2x))dx

Evaluate: (i) int tan^(-1)((sin2x)/(1+cos2x))dx( ii) int cos^(-1)(sin x)dx

int tan^-1((sin x)/(1+ cos x)) dx =

Evaluate: (i) int cot^(-1)((sin2x)/(1-cos2x))dx (ii) int sin^(-1)((2tan x)/(1+tan^(2)x))dx

(i) int e^(2x) ((1+sin2x)/(1+cos2x)) dx (ii) int e^(2x) ((sin4x-2)/(1-cos4x))

If I_(1) int sin^(-1) ((2x)/(1 +x^(2)) ) dx , I_(2) = int cos^(-1) ((1-x^(2))/(1 +x^(2)) ) dx , I_(3) = int tan^(-1) ((2x)/(1 - x^(2)) ) dx , then I_(1) + I_(2) - I_(3) =

int(sin2x)/(1+cos x)^2dx

Evaluate: int e^(2x)((1+sin2x)/(1+cos2x))dx

Evaluate: int e^(2x)((1-sin2x)/(1-cos2x))dx