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

The integral of (e^x)/2 is 1/2 e^x+C

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integral of (e^x)/2

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

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

Add a constant to the solution

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

\frac{d}{d t} (a cos (2 t) + b sin (2 t))

\int sin^{2} (x - y) d y

y = x^{2} + 2 x + 10, at x = 6

\frac{d y}{d x} = 2 y + x^{2} e^{2 x} + 5

x \to 0 lim (2400 x - 2 x^{2})