What is the integral from 2 to 7 of (8x)/(x^2+1) ?

The integral from 2 to 7 of (8x)/(x^2+1) is 4ln(10)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 7 of (8x)/(x^2+1)

\int_{2}^{7} \frac{8 x}{x ^{2} + 1} d x

4 ln (10)

Decimal

9.21034 \dots

Solution steps

\int_{2}^{7} \frac{8 x}{x ^{2} + 1} d x

Take the constant out:

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

= 8 \cdot \int_{2}^{7} \frac{x}{x ^{2} + 1} d x

Apply u-substitution

: \int_{5}^{50} \frac{1}{2 u} d u

= 8 \cdot \int_{5}^{50} \frac{1}{2 u} d u

Take the constant out:

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

= 8 \cdot \frac{1}{2} \cdot \int_{5}^{50} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 8 \cdot \frac{1}{2} [ln ∣ u ∣]_{5}^{50}

Simplify

8 \cdot \frac{1}{2} [ln ∣ u ∣]_{5}^{50} : 4 [ln ∣ u ∣]_{5}^{50}

= 4 [ln ∣ u ∣]_{5}^{50}

Compute the boundaries:

ln (50) - ln (5)

= 4 (ln (50) - ln (5))

Simplify

= 4 ln (10)

\int_{0}^{1} (x - 1)^{3} d x

\int_{0}^{x} x cos (x) d x

\int_{0}^{1} x 56 x^{2} + 25 d x

\int_{- \frac{5 π}{6}}^{0} sin (x) d x

\int_{- 3}^{3} (y + 2 ∣ y ∣) d y

What is the integral from 2 to 7 of (8x)/(x^2+1) ?
The integral from 2 to 7 of (8x)/(x^2+1) is 4ln(10)