What is the integral of (e^{-x/4}+e^{x/2}) ?

The integral of (e^{-x/4}+e^{x/2}) is -4e^{-x/4}+2e^{x/2}+C

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integral of (e^{-x/4}+e^{x/2})

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

- 4 e^{- \frac{x}{4}} + 2 e^{\frac{x}{2}} + C

Solution steps

\int e^{- \frac{x}{4}} + e^{\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 e^{- \frac{x}{4}} d x + \int e^{\frac{x}{2}} d x

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

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

= - 4 e^{- \frac{x}{4}} + 2 e^{\frac{x}{2}}

Add a constant to the solution

= - 4 e^{- \frac{x}{4}} + 2 e^{\frac{x}{2}} + C

(x + 1) \frac{d y}{d x} = (x + 6)

x \to 3 lim (\frac{x}{2} + 1)

\int \frac{1}{( 5 x + 2 ) ^{3}} d x

\frac{\partial}{\partial y} (x e^{5 x y})

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} + \frac{1}{2})

What is the integral of (e^{-x/4}+e^{x/2}) ?
The integral of (e^{-x/4}+e^{x/2}) is -4e^{-x/4}+2e^{x/2}+C