What is the integral from 1 to 8 of 3/x ?

The integral from 1 to 8 of 3/x is 9ln(2)

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integral from 1 to 8 of 3/x

\int_{1}^{8} \frac{3}{x} d x

9 ln (2)

Decimal

6.23832 \dots

Solution steps

\int_{1}^{8} \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}^{8} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 [ln ∣ x ∣]_{1}^{8}

Compute the boundaries:

3 ln (2)

= 3 \cdot 3 ln (2)

Simplify

= 9 ln (2)

\int \frac{( x ^{2} )}{( 15 + 6 x - 9 x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (e^{x^{\frac{1}{2}}})

f (x) = 2 x^{3} - 3 x^{2} + 3, at x = 1

\frac{1}{2 x ^{6}}

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

What is the integral from 1 to 8 of 3/x ?
The integral from 1 to 8 of 3/x is 9ln(2)