How do you find the integral of $int 1/(1 + cos(x))$ ?

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Answer 1 · 2015-09-18T18:30:20

$-cotx+cscx+"C"$

$int1/(1+cosx)dx = int(1-cosx)/((1+cosx)(1-cosx))dx$

$= int(1-cosx)/(1-cos^2x)dx$

$= int(1-cosx)/sin^2xdx$

$= int 1/sin^2xdx-intcosx/sin^2xdx$

= $int csc^2xdx-intcotxcscxdx$

= $-cotx+cscx+"C"$

How do you find the integral of int 1/(1 + cos(x))int 1/(1 + cos(x))?