What is the integral of (3^{sqrt(x)})/(sqrt(x)) ?

The integral of (3^{sqrt(x)})/(sqrt(x)) is (2*3^{sqrt(x)})/(ln(3))+C

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integral of (3^{sqrt(x)})/(sqrt(x))

\int \frac{3 ^{x}}{x} d x

\frac{2 \cdot 3 ^{x}}{ln ( 3 )} + C

Solution steps

\int \frac{3 ^{x}}{x} d x

Apply u-substitution

: \int 2 \cdot 3^{u} d u

= \int 2 \cdot 3^{u} d u

Take the constant out:

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

= 2 \cdot \int 3^{u} d u

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

= 2 \cdot \frac{3 ^{u}}{ln ( 3 )}

Substitute back

u = x

= 2 \cdot \frac{3 ^{x}}{ln ( 3 )}

Multiply fractions:

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

= \frac{2 \cdot 3 ^{x}}{ln ( 3 )}

Add a constant to the solution

= \frac{2 \cdot 3 ^{x}}{ln ( 3 )} + C

3 y^{^{''}} + 8 y^{^{'}} - 3 y = 0

\int (1 + cos^{2} (x)) d x

n = 1 \sum \infty \frac{7 ^{n}}{6 ^{n}}

x \to \infty lim (5 e^{- t} i - \frac{5 t}{t + 7} j + 5 arctan (t k))

y^{^{'}} = - 6 y

What is the integral of (3^{sqrt(x)})/(sqrt(x)) ?
The integral of (3^{sqrt(x)})/(sqrt(x)) is (2*3^{sqrt(x)})/(ln(3))+C