What is the integral of (2^{-sqrt(x)})/(sqrt(x)) ?

The integral of (2^{-sqrt(x)})/(sqrt(x)) is -(2^{-sqrt(x)+1})/(ln(2))+C

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integral of (2^{-sqrt(x)})/(sqrt(x))

\int \frac{2 ^{- x}}{x} d x

- \frac{2 ^{- x + 1}}{ln ( 2 )} + C

Solution steps

\int \frac{2 ^{- x}}{x} d x

Apply u-substitution

: \int 2^{- u + 1} d u

= \int 2^{- u + 1} d u

Apply u-substitution

: \int - 2^{v} d v

= \int - 2^{v} d v

Take the constant out:

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

= - \int 2^{v} d v

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

= - \frac{2 ^{v}}{ln ( 2 )}

Substitute back

= - \frac{2 ^{- x + 1}}{ln ( 2 )}

Add a constant to the solution

= - \frac{2 ^{- x + 1}}{ln ( 2 )} + C

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What is the integral of (2^{-sqrt(x)})/(sqrt(x)) ?
The integral of (2^{-sqrt(x)})/(sqrt(x)) is -(2^{-sqrt(x)+1})/(ln(2))+C