What is the integral of-sin(x)+e^x ?

The integral of-sin(x)+e^x is cos(x)+e^x+C

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integral of-sin(x)+e^x

\int - sin (x) + e^{x} d x

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

Solution steps

\int - sin (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 sin (x) d x + \int e^{x} d x

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

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

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

Simplify

= cos (x) + e^{x}

Add a constant to the solution

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

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