What is the integral of (e^{6sqrt(x)})/(sqrt(x)) ?

The integral of (e^{6sqrt(x)})/(sqrt(x)) is 1/3 e^{6sqrt(x)}+C

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integral of (e^{6sqrt(x)})/(sqrt(x))

\int \frac{e ^{6 x}}{x} d x

\frac{1}{3} e^{6 x} + C

Solution steps

\int \frac{e ^{6 x}}{x} d x

Apply u-substitution

: \int \frac{e ^{u}}{3} d u

= \int \frac{e ^{u}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{3} e^{u}

Substitute back

u = 6 x

= \frac{1}{3} e^{6 x}

Add a constant to the solution

= \frac{1}{3} e^{6 x} + C

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What is the integral of (e^{6sqrt(x)})/(sqrt(x)) ?
The integral of (e^{6sqrt(x)})/(sqrt(x)) is 1/3 e^{6sqrt(x)}+C