How will I solve this without substitution?

The integral is (1 + sin^2theta csctheta)d theta(1+sin2θcscθ)dθ

2 Answers
MoominDave
Jun 5, 2018

Simplify using standard trig definitions

Explanation:

Recall the definition of csccsc as csctheta=1/sinthetacscθ=1sinθ. So this expression simplifies to be int1+sinthetad theta=theta-costheta+C∫1+sinθdθ=θ−cosθ+C

Daniel L.
Jun 5, 2018

See explanation.

Explanation:

According to the definition of csc thetacscθ we have:

csc theta=1/sinthetacscθ=1sinθ

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∫(1+sin2θsinθ)dθ=∫(1+sinθ)dθ=θ−cosθ+C

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