What is the integral of 4e^x+cos(x/5) ?

The integral of 4e^x+cos(x/5) is 4e^x+5sin(x/5)+C

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integral of 4e^x+cos(x/5)

\int 4 e^{x} + cos (\frac{x}{5}) d x

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

Solution steps

\int 4 e^{x} + cos (\frac{x}{5}) 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 4 e^{x} d x + \int cos (\frac{x}{5}) d x

\int 4 e^{x} d x = 4 e^{x}

\int cos (\frac{x}{5}) d x = 5 sin (\frac{x}{5})

= 4 e^{x} + 5 sin (\frac{x}{5})

Add a constant to the solution

= 4 e^{x} + 5 sin (\frac{x}{5}) + C

What is the integral of 4e^x+cos(x/5) ?
The integral of 4e^x+cos(x/5) is 4e^x+5sin(x/5)+C