What is the integral of (sin(x)+10csc^2(x)) ?

The integral of (sin(x)+10csc^2(x)) is -cos(x)-10cot(x)+C

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integral of (sin(x)+10csc^2(x))

\int (sin (x) + 10 csc^{2} (x)) d x

- cos (x) - 10 cot (x) + C

Solution steps

\int sin (x) + 10 csc^{2} (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 sin (x) d x + \int 10 csc^{2} (x) d x

\int sin (x) d x = - cos (x)

\int 10 csc^{2} (x) d x = - 10 cot (x)

= - cos (x) - 10 cot (x)

Add a constant to the solution

= - cos (x) - 10 cot (x) + C

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What is the integral of (sin(x)+10csc^2(x)) ?
The integral of (sin(x)+10csc^2(x)) is -cos(x)-10cot(x)+C