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

Answer 1

Christopher Allers

#-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"#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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