What is the integral of (e^1)/x ?

The integral of (e^1)/x is eln|x|+C

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integral of (e^1)/x

integral

\frac{e ^{1}}{x}

e ln ∣ x ∣ + C

Solution steps

\int \frac{e ^{1}}{x} d x

Take the constant out:

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

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

Simplify

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= e ln ∣ x ∣

Add a constant to the solution

= e ln ∣ x ∣ + C

1 + tan^{2} (x)

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

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

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

x^{2} (e^{- x})^{2}