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

1 Answer

Dharma R. · John D.

Sep 18, 2015

#-cotx+cscx+"C"#

Explanation:

#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"#

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