What is the integral of (e^3)/x ?

The integral of (e^3)/x is e^3ln|x|+C

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integral of (e^3)/x

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

e^{3} ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

= e^{3} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= e^{3} ln ∣ x ∣

Add a constant to the solution

= e^{3} ln ∣ x ∣ + C

x \to 0 lim (\frac{∣ x ∣}{4 x})

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