What is the integral of csc^2(y)+1 ?

The integral of csc^2(y)+1 is -cot(y)+y+C

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integral of csc^2(y)+1

\int csc^{2} (y) + 1 d y

- cot (y) + y + C

Solution steps

\int csc^{2} (y) + 1 d y

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} (y) d y + \int 1 d y

\int csc^{2} (y) d y = - cot (y)

\int 1 d y = y

= - cot (y) + y

Add a constant to the solution

= - cot (y) + y + C