What is the integral of (7csc^2(x)-8e^x) ?

The integral of (7csc^2(x)-8e^x) is -7cot(x)-8e^x+C

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integral of (7csc^2(x)-8e^x)

\int (7 csc^{2} (x) - 8 e^{x}) d x

- 7 cot (x) - 8 e^{x} + C

Solution steps

\int 7 csc^{2} (x) - 8 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 7 csc^{2} (x) d x - \int 8 e^{x} d x

\int 7 csc^{2} (x) d x = - 7 cot (x)

\int 8 e^{x} d x = 8 e^{x}

= - 7 cot (x) - 8 e^{x}

Add a constant to the solution

= - 7 cot (x) - 8 e^{x} + C

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What is the integral of (7csc^2(x)-8e^x) ?
The integral of (7csc^2(x)-8e^x) is -7cot(x)-8e^x+C