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:

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