What is the integral from 1 to 9 of 6/x ?

The integral from 1 to 9 of 6/x is 12ln(3)

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integral from 1 to 9 of 6/x

\int_{1}^{9} \frac{6}{x} d x

12 ln (3)

Decimal

13.18334 \dots

Solution steps

\int_{1}^{9} \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}^{9} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 6 [ln ∣ x ∣]_{1}^{9}

Compute the boundaries:

2 ln (3)

= 6 \cdot 2 ln (3)

Simplify

= 12 ln (3)

\int_{- 1}^{3} (2 x - 3) d x

\int_{- 3}^{0} 3 + 9 - x^{2} d x

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

\int_{0}^{π} 2 e^{x} - 7 cos (x) d x

What is the integral from 1 to 9 of 6/x ?
The integral from 1 to 9 of 6/x is 12ln(3)