What is the integral of-8cot(x)csc(x)+5e^x ?

The integral of-8cot(x)csc(x)+5e^x is 8csc(x)+5e^x+C

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integral of-8cot(x)csc(x)+5e^x

\int - 8 cot (x) csc (x) + 5 e^{x} d x

8 csc (x) + 5 e^{x} + C

Solution steps

\int - 8 cot (x) csc (x) + 5 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 8 cot (x) csc (x) d x + \int 5 e^{x} d x

\int 8 cot (x) csc (x) d x = - 8 csc (x)

\int 5 e^{x} d x = 5 e^{x}

= - (- 8 csc (x)) + 5 e^{x}

Simplify

= 8 csc (x) + 5 e^{x}

Add a constant to the solution

= 8 csc (x) + 5 e^{x} + C

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What is the integral of-8cot(x)csc(x)+5e^x ?
The integral of-8cot(x)csc(x)+5e^x is 8csc(x)+5e^x+C