What is the integral from 1 to 10 of 5/x ?

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

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integral from 1 to 10 of 5/x

\int_{1}^{10} \frac{5}{x} d x

5 ln (10)

Decimal

11.51292 \dots

Solution steps

\int_{1}^{10} \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}^{10} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{1}^{10}

Compute the boundaries:

ln (10)

= 5 ln (10)

\int_{0}^{2} (x^{2} - 10 x + 16) d x

\int_{0}^{\infty} 2 e^{- 2 y} d y

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

\int_{2}^{\infty} - 4 x^{- 2} d x

\int_{0}^{x} t d t

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