What is the integral from 1 to 8 of (14x)/(x^2+6) ?

The integral from 1 to 8 of (14x)/(x^2+6) is 7ln(10)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to 8 of (14x)/(x^2+6)

\int_{1}^{8} \frac{14 x}{x ^{2} + 6} d x

7 ln (10)

Decimal

16.11809 \dots

Solution steps

\int_{1}^{8} \frac{14 x}{x ^{2} + 6} d x

Take the constant out:

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

= 14 \cdot \int_{1}^{8} \frac{x}{x ^{2} + 6} d x

Apply u-substitution

= 14 \cdot \int_{7}^{70} \frac{1}{2 u} d u

Take the constant out:

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

= 14 \cdot \frac{1}{2} \cdot \int_{7}^{70} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 14 \cdot \frac{1}{2} [ln ∣ u ∣]_{7}^{70}

Simplify

14 \cdot \frac{1}{2} [ln ∣ u ∣]_{7}^{70} : 7 [ln ∣ u ∣]_{7}^{70}

= 7 [ln ∣ u ∣]_{7}^{70}

Compute the boundaries:

ln (70) - ln (7)

= 7 (ln (70) - ln (7))

Simplify

= 7 ln (10)

What is the integral from 1 to 8 of (14x)/(x^2+6) ?
The integral from 1 to 8 of (14x)/(x^2+6) is 7ln(10)