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Question

Integrate the following function 11+cotx

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Solution

dx1+cotx=sinxsinx+cosxdx

=122sinxsinx+cosxdx

=12(2sinxsinx+cosx1+1)dx

=12(2sinxsinx+cosxsinx+cosxsinx+cosx+1)dx

=12(sinxcosxsinx+cosx+1)dx

=12log|sinx+cosx|+12x+c

Formula:
f(x)f(x)dx=logf(x)+c

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