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

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

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

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

2 e^{x + 4} + C

Solution steps

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

Apply u-substitution

: \int 2 e^{u} d u

= \int 2 e^{u} d u

Take the constant out:

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

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

Use the common integral:

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

= 2 e^{u}

Substitute back

u = x + 4

= 2 e^{x + 4}

Add a constant to the solution

= 2 e^{x + 4} + C

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