How will I solve this without substitution?

Question

The integral is #(1 + sin^2theta csctheta)d theta#

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Answer 1 · 2018-06-05T20:32:50

Simplify using standard trig definitions

Recall the definition of #csc# as #csctheta=1/sintheta#. So this expression simplifies to be #int1+sinthetad theta=theta-costheta+C#

Answer 2 · 2018-06-05T20:35:43

See explanation.

According to the definition of #csc theta# we have:

If we use this identity, then the integral is:

#int (1+sin^2theta/sintheta)d theta= int(1+sintheta)d theta=theta -cos theta+C#