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

y (x + 1) + y^{^{'}} = 0, y (- 2) = 1

\frac{\partial}{\partial y} (2 x^{3} y)

\frac{d}{d x} (x^{2} y + 4 y)

x = 0, y = 0, y = \frac{- x ^{2} + 8}{9}

θ \to 0 lim (\frac{θ}{sin ( θ )})

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