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

The integral of (1+sin^2(x)csc(x)) is x-cos(x)+C

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integral of (1+sin^2(x)csc(x))

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

x - cos (x) + C

Solution steps

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

Apply the Sum Rule:

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

= \int 1 d x + \int sin^{2} (x) csc (x) d x

\int 1 d x = x

\int sin^{2} (x) csc (x) d x = - cos (x)

= x - cos (x)

Add a constant to the solution

= x - cos (x) + C

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What is the integral of (1+sin^2(x)csc(x)) ?
The integral of (1+sin^2(x)csc(x)) is x-cos(x)+C