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

The integral of (a^{sqrt(x)})/(sqrt(x)) is (2a^{sqrt(x)})/(ln(a))+C

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integral of (a^{sqrt(x)})/(sqrt(x))

\int \frac{a ^{x}}{x} d x

\frac{2 a ^{x}}{ln ( a )} + C

Solution steps

\int \frac{a ^{x}}{x} d x

Apply u-substitution

: \int 2 a^{u} d u

= \int 2 a^{u} d u

Take the constant out:

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

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

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 2 \cdot \frac{a ^{u}}{ln ( a )}

Substitute back

u = x

= 2 \cdot \frac{a ^{x}}{ln ( a )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 a ^{x}}{ln ( a )}

Add a constant to the solution

= \frac{2 a ^{x}}{ln ( a )} + C

\frac{d}{d θ} (ln (θ + 1))

\frac{d}{d y} (e^{y} + \frac{y}{x})

\int cot^{4} (x cs) c^{2} x d x

\int cot^{3} (θ) csc^{2} (θ) d θ

\frac{d ^{2} y}{d t ^{2}} + 3 (\frac{d y}{d t}) + 2 y = 1

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