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

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

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Answer 1 · 2015-09-18T18:40:27

#x+secx-tanx+c#

Explanation:

# int1/(1+cscx)dx=intsinx/(1+sinx)dx=int(sinx-sin^2x)/(cos^2x)dx#
=#inttanxsecxdx-inttan^2xdx#
=#inttanxsecxdx-int (sec^2x-1)dx#
=#secx-(tanx-x)+c#
=#x+secx-tanx+c#

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

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