What is the integral of (e^{2x+1})/2 ?

The integral of (e^{2x+1})/2 is 1/4 e^{2x+1}+C

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integral of (e^{2x+1})/2

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

\frac{1}{4} e^{2 x + 1} + C

Solution steps

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

Apply u-substitution

: \int e^{u} \frac{1}{2} d u

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} \cdot \frac{1}{2} e^{u}

Substitute back

u = 2 x + 1

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

Simplify

\frac{1}{2} \cdot \frac{1}{2} e^{2 x + 1} : \frac{1}{4} e^{2 x + 1}

= \frac{1}{4} e^{2 x + 1}

Add a constant to the solution

= \frac{1}{4} e^{2 x + 1} + C

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What is the integral of (e^{2x+1})/2 ?
The integral of (e^{2x+1})/2 is 1/4 e^{2x+1}+C