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Question

What is cosecxintegration.


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Solution

Finding the integration of cosecx:

Multiply and divide the integrand with cosecxā€“cotx

āˆ«cosecxdx=āˆ«cosecxƗcosecxā€“cotxcosecxā€“cotxdx=āˆ«cosec2xā€“cosecxcotxcosecxā€“cotxdx...(1)

Let,

cosecx-cotx=tā‡’-cosecxcotx+cosec2xdx=dt.

Now, substitute the above values in the .eq.(1):

āˆ«cosecxdx=āˆ«dtt=logt+c[āˆµāˆ«dxx=lnx]=logcosecx-cotx+c

Thus, the integral of cosecx is log|cosecx-cotx|+c.


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