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

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

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integral of (e^{4sqrt(r)})/(sqrt(r))

\int \frac{e ^{4 r}}{r} d r

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

Solution steps

\int \frac{e ^{4 r}}{r} d r

Apply u-substitution

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

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

Use the common integral:

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

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

Substitute back

u = 4 r

= \frac{1}{2} e^{4 r}

Add a constant to the solution

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

x \to - 3 - lim (\frac{x + 4}{x + 3})

\int \frac{1}{7 - 6 x} d x

x \to 5 - lim (\frac{x + 1}{x - 5})

f (x) = - cos (x)

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

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