What is the integral of (e^{9sqrt(x)})/(sqrt(x)) ?

The integral of (e^{9sqrt(x)})/(sqrt(x)) is 2/9 e^{9sqrt(x)}+C

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integral of (e^{9sqrt(x)})/(sqrt(x))

\int \frac{e ^{9 x}}{x} d x

\frac{2}{9} e^{9 x} + C

Solution steps

\int \frac{e ^{9 x}}{x} d x

Apply u-substitution

: \int \frac{2 e ^{u}}{9} d u

= \int \frac{2 e ^{u}}{9} d u

Take the constant out:

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

= \frac{2}{9} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{2}{9} e^{u}

Substitute back

u = 9 x

= \frac{2}{9} e^{9 x}

Add a constant to the solution

= \frac{2}{9} e^{9 x} + C

\frac{d}{d x} (cos (ln (9 x)))

\frac{d}{d x} (e^{x} (13 x^{2} - 26 x + 26))

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 0

\frac{\partial}{\partial x} (y sin (\frac{x}{y}))

f (x) = \frac{x ^{2} - 6 x + 1}{x ^{2} + 4}

What is the integral of (e^{9sqrt(x)})/(sqrt(x)) ?
The integral of (e^{9sqrt(x)})/(sqrt(x)) is 2/9 e^{9sqrt(x)}+C