What is the integral of (-e^{-ln(x)})/x ?

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

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integral of (-e^{-ln(x)})/x

\int \frac{- e ^{- l n (x)}}{x} d x

\frac{1}{x} + C

Solution steps

\int \frac{- e ^{- l n (x)}}{x} d x

Take the constant out:

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

= - \int \frac{e ^{- l n (x)}}{x} d x

Simplify

\frac{e ^{- l n (x)}}{x} : \frac{1}{x ^{2}}

= - \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

= - (- \frac{1}{x})

Simplify

= \frac{1}{x}

Add a constant to the solution

= \frac{1}{x} + C

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