What is the integral from-e^2 to-e of 3/x ?

The integral from-e^2 to-e of 3/x is -3

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integral from-e^2 to-e of 3/x

\int_{- e^{2}}^{- e} \frac{3}{x} d x

- 3

Solution steps

\int_{- e^{2}}^{- e} \frac{3}{x} d x

Take the constant out:

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

= 3 \cdot \int_{- e^{2}}^{- e} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 [ln ∣ x ∣]_{- e^{2}}^{- e}

Compute the boundaries:

- 1

= 3 (- 1)

Simplify

= - 3

\int \frac{1}{x ^{2} + 4 x + 3} d x

sin (x y)

f (x) = (x^{3} - 4 x)^{8}, (2, 0)

\int (3 y - 2 y^{- 3}) d y

x \to \infty lim (\frac{ln ( 3 x + 5 )}{ln ( 7 x + 3 ) + 1})

What is the integral from-e^2 to-e of 3/x ?
The integral from-e^2 to-e of 3/x is -3