What is the integral of 1-csc(x)cot(x)+e^x ?

The integral of 1-csc(x)cot(x)+e^x is x+csc(x)+e^x+C

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integral of 1-csc(x)cot(x)+e^x

\int 1 - csc (x) cot (x) + e^{x} d x

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

Solution steps

\int 1 - csc (x) cot (x) + 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 1 d x - \int csc (x) cot (x) d x + \int e^{x} d x

\int 1 d x = x

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

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

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

Simplify

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

Add a constant to the solution

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

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What is the integral of 1-csc(x)cot(x)+e^x ?
The integral of 1-csc(x)cot(x)+e^x is x+csc(x)+e^x+C