What is the integral from 1 to 9 of 5/x ?

The integral from 1 to 9 of 5/x is 10ln(3)

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integral from 1 to 9 of 5/x

\int_{1}^{9} \frac{5}{x} d x

10 ln (3)

Decimal

10.98612 \dots

Solution steps

\int_{1}^{9} \frac{5}{x} d x

Take the constant out:

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

= 5 \cdot \int_{1}^{9} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{1}^{9}

Compute the boundaries:

2 ln (3)

= 5 \cdot 2 ln (3)

Simplify

= 10 ln (3)

\int_{x}^{0} e^{- 6 t} d t

\int_{0}^{\frac{π}{2}} \frac{2}{3} sin (θ) d θ

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

\int_{- \frac{π}{2}}^{π} 9 cos (x) d x

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

What is the integral from 1 to 9 of 5/x ?
The integral from 1 to 9 of 5/x is 10ln(3)