What is the integral from 1 to 4 of 6/x ?

The integral from 1 to 4 of 6/x is 12ln(2)

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integral from 1 to 4 of 6/x

\int_{1}^{4} \frac{6}{x} d x

12 ln (2)

Decimal

8.31776 \dots

Solution steps

\int_{1}^{4} \frac{6}{x} d x

Take the constant out:

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

= 6 \cdot \int_{1}^{4} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 6 [ln ∣ x ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= 6 \cdot 2 ln (2)

Simplify

= 12 ln (2)

\int \frac{3 x - 2}{x ^{5}} d x

\frac{d}{d x} (2 cos (x) - x sin (x))

n = 0 \sum \infty (\frac{6}{7})^{n}

\frac{d y}{d x} + 12 y = 4

(2 x y^{2} + 2 y) d x + (2 x^{2} y + 2 x) d y = 0, y (1) = 2

What is the integral from 1 to 4 of 6/x ?
The integral from 1 to 4 of 6/x is 12ln(2)