What is the integral of (5e^{5sqrt(x)})/(sqrt(x)) ?

The integral of (5e^{5sqrt(x)})/(sqrt(x)) is 2e^{5sqrt(x)}+C

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integral of (5e^{5sqrt(x)})/(sqrt(x))

\int \frac{5 e ^{5 x}}{x} d x

2 e^{5 x} + C

Solution steps

\int \frac{5 e ^{5 x}}{x} d x

Take the constant out:

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

= 5 \cdot \int \frac{e ^{5 x}}{x} d x

Apply u-substitution

: \int \frac{2 e ^{u}}{5} d u

= 5 \cdot \int \frac{2 e ^{u}}{5} d u

Take the constant out:

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

= 5 \cdot \frac{2}{5} \cdot \int e^{u} d u

Use the common integral:

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

= 5 \cdot \frac{2}{5} e^{u}

Substitute back

u = 5 x

= 5 \cdot \frac{2}{5} e^{5 x}

Simplify

5 \cdot \frac{2}{5} e^{5 x} : 2 e^{5 x}

= 2 e^{5 x}

Add a constant to the solution

= 2 e^{5 x} + C

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What is the integral of (5e^{5sqrt(x)})/(sqrt(x)) ?
The integral of (5e^{5sqrt(x)})/(sqrt(x)) is 2e^{5sqrt(x)}+C