What is the integral of 5e^x+cos(x/2) ?

The integral of 5e^x+cos(x/2) is 5e^x+2sin(x/2)+C

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integral of 5e^x+cos(x/2)

\int 5 e^{x} + cos (\frac{x}{2}) d x

5 e^{x} + 2 sin (\frac{x}{2}) + C

Solution steps

\int 5 e^{x} + cos (\frac{x}{2}) 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 5 e^{x} d x + \int cos (\frac{x}{2}) d x

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

\int cos (\frac{x}{2}) d x = 2 sin (\frac{x}{2})

= 5 e^{x} + 2 sin (\frac{x}{2})

Add a constant to the solution

= 5 e^{x} + 2 sin (\frac{x}{2}) + C

What is the integral of 5e^x+cos(x/2) ?
The integral of 5e^x+cos(x/2) is 5e^x+2sin(x/2)+C