Integrating 1/(1+cos(x)+sin(x)) with Weierstrass substitution

[Alexx1]

Is this correct:

integral: 1/(1+cos(x)+sin(x)) dx

t = tan(x/2) --> x = 2arctan(t) --> dx = 2/(1+t^2) dt

sin(x) = 2t/(1+t^2)
cos(x) = (1-t^2)/(1+t^2)

1/(1+cos(x)+sin(x)) dx

= ...

= 2 integral 1/(2(1+t)) dt = integral 1/(1+t) dt = ln (1+t) = ln(1+tan(x/2))

 

[arildno]

Try to differntiate your putative answer!