What is the integral of 4e^x+cos(x/2) ?

The integral of 4e^x+cos(x/2) is 4e^x+2sin(x/2)+C

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integral of 4e^x+cos(x/2)

\int 4 e^{x} + cos (\frac{x}{2}) d x

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

Solution steps

\int 4 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 4 e^{x} d x + \int cos (\frac{x}{2}) d x

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

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

= 4 e^{x} + 2 sin (\frac{x}{2})

Add a constant to the solution

= 4 e^{x} + 2 sin (\frac{x}{2}) + C

\frac{d}{d x} ((- 25 x^{2} + 1)^{2})

\frac{\partial}{\partial x} (- \frac{7 x ^{2}}{( x - y ) ^{2}})

\frac{d}{d x} (a x^{b^{2} - c})

\frac{\partial}{\partial x} (x y + 2 z)

f (x) = x^{- \frac{1}{5}} + x^{\frac{1}{5}}

What is the integral of 4e^x+cos(x/2) ?
The integral of 4e^x+cos(x/2) is 4e^x+2sin(x/2)+C