How do I integrate the function f(x)=cos(x)/(sin^2(x))+sin(x)f(x)=cos(x)sin2(x)+sin(x)?

2 Answers
Mar 19, 2015

Try this:
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Mar 19, 2015

Rewrite cosx/sin^2xcosxsin2x and then integrate term by term.

cosx/sin^2x=1/sinx cosx/sinx=cscxcotxcosxsin2x=1sinxcosxsinx=cscxcotx So,

int (cosx/sin^2x+sinx)dx=intcscxcotx dx+int sinx dx(cosxsin2x+sinx)dx=cscxcotxdx+sinxdx

=-cscx-cosx+C=cscxcosx+C.