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

integral

\frac{e ^{3}}{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

\frac{x ^{0.5}}{( 1 + x ) ^{2}}

\frac{x}{( ( x - 1 ) ( x - 2 ) ( x - 3 ) )}

\frac{cot ( x )}{2}

(a - x^{2})^{\frac{1}{2}}

sin^{3} (x) cos^{3} (x)