What is the integral of csc^2(x)-2e^x ?

The integral of csc^2(x)-2e^x is -cot(x)-2e^x+C

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integral of csc^2(x)-2e^x

\int csc^{2} (x) - 2 e^{x} d x

- cot (x) - 2 e^{x} + C

Solution steps

\int csc^{2} (x) - 2 e^{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 csc^{2} (x) d x - \int 2 e^{x} d x

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

\int 2 e^{x} d x = 2 e^{x}

= - cot (x) - 2 e^{x}

Add a constant to the solution

= - cot (x) - 2 e^{x} + C

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