What is the integral of csc^2(θ)+3 ?

The integral of csc^2(θ)+3 is -cot(θ)+3θ+C

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integral of csc^2(θ)+3

\int csc^{2} (θ) + 3 d θ

- cot (θ) + 3 θ + C

Solution steps

\int csc^{2} (θ) + 3 d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int csc^{2} (θ) d θ + \int 3 d θ

\int csc^{2} (θ) d θ = - cot (θ)

\int 3 d θ = 3 θ

= - cot (θ) + 3 θ

Add a constant to the solution

= - cot (θ) + 3 θ + C

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