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Question

Integrate cotxcosxdx.


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Solution

Solve the given integral

Given: cotxcosxdx

We know that,

cotx=cosxsinx

and,

sin2x+cos2x=1cos2x=1-sin2x

Now, cotxcosxdx can be written as,

=cosxsinxcosxdx

=cos2xsinxdx=1-sin2xsinxdx=dxsinx-sinxdx=cosecxdx+cosx=-lncosecx-cotx+cosx+C

Hence, the Integral of cotxcosxdx is -lncosecx-cotx+cosx+C, where C is an arbitrary constant.


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