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

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

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integral of e^{-ln(x)}

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

ln ∣ x ∣ + C

Solution steps

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

Simplify

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

= \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= ln ∣ x ∣

Add a constant to the solution

= ln ∣ x ∣ + C

x = y^{2}, x = y + 2

y^{^{'}} = e^{(3 x + 2 y)}

\frac{\partial}{\partial x} ((x^{4} + 3 x^{2}) \cdot (1 - 5 x))

\int \frac{e ^{x}}{( 7 - e ^{x} ) ^{2}} d x