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by Mukss

2015-11-11T06:30:09+05:30

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Compute the indefinite integral ∫cos(x)/(1+sin(x)+cos(x)).
= arctan(tan(x/2)) - (1/2) ln(tan^2(x/2) + 1) + C.
Then compute the boundaries.
= 1/4 * (π - ln(4)) - 0
= 1/4 * (π - ln(4))
the second line, integrand is correct. But is it in a some what complex form. It could be simplified further.
2015-11-11T22:08:44+05:30

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Integral of

You could also express cos x and sin x  in terms of  tan x/2  and  then  say u = tan x/2.  Express integrand in terms of  u.  and integrate that.

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