What is the integral of e^{2x}-1/2 e^{x/2} ?

The integral of e^{2x}-1/2 e^{x/2} is 1/2 e^{2x}-e^{x/2}+C

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integral of e^{2x}-1/2 e^{x/2}

\int e^{2 x} - \frac{1}{2} e^{\frac{x}{2}} d x

\frac{1}{2} e^{2 x} - e^{\frac{x}{2}} + C

Solution steps

\int e^{2 x} - \frac{1}{2} 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^{2 x} d x - \int \frac{1}{2} e^{\frac{x}{2}} d x

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

\int \frac{1}{2} e^{\frac{x}{2}} d x = e^{\frac{x}{2}}

= \frac{1}{2} e^{2 x} - e^{\frac{x}{2}}

Add a constant to the solution

= \frac{1}{2} e^{2 x} - e^{\frac{x}{2}} + C

\frac{d}{d x} (e^{- x} + \frac{x}{3})

x \to \infty lim (∣ x ∣)

\int \frac{1}{( 3 x + 4 ) ( 4 x - 1 )} d x

\frac{d}{d x} (4 x^{5} - 3 x^{4} + 2 x^{3} - x + 100)

(1 - x) d y - y^{2} d x = 0

What is the integral of e^{2x}-1/2 e^{x/2} ?
The integral of e^{2x}-1/2 e^{x/2} is 1/2 e^{2x}-e^{x/2}+C