What is the integral of # [ (1+cos^2(x)) / sin(x) ] dx#?

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Answer 1 · 2016-08-06T23:38:41

#= -2 ln | csc x - cot x| + cos x + C#

#int (1+cos^2(x)) / sin(x) dx#

is just crying out for the application of the Pythagorean identity

#=int (1+ color(red)(1 - sin^2 x)) / sin(x) dx#

#=int (2 - sin^2 x) / sin(x) dx#

#=int 2 csc x - sin x dx#

these are well known integrals

#= -2 ln | csc x - cot x| + cos x + C#