What is the integral from 1 to 9 of 3/x ?

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

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integral from 1 to 9 of 3/x

\int_{1}^{9} \frac{3}{x} d x

6 ln (3)

Decimal

6.59167 \dots

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 [ln ∣ x ∣]_{1}^{9}

Compute the boundaries:

2 ln (3)

= 3 \cdot 2 ln (3)

Simplify

= 6 ln (3)

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

\int_{0}^{\frac{a}{2}} x sin (\frac{nπ x}{a}) d x

\int_{- 2}^{2} 2 - x d x

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

\int_{0}^{2} (6 x - 3) (4 x^{2} + 4) d x

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