What is the integral of (2e^x+sin(x)-cos(x)) ?

The integral of (2e^x+sin(x)-cos(x)) is 2e^x-cos(x)-sin(x)+C

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integral of (2e^x+sin(x)-cos(x))

\int (2 e^{x} + sin (x) - cos (x)) d x

2 e^{x} - cos (x) - sin (x) + C

Solution steps

\int 2 e^{x} + sin (x) - cos (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 2 e^{x} d x + \int sin (x) d x - \int cos (x) d x

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

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

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

= 2 e^{x} - cos (x) - sin (x)

Add a constant to the solution

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

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