What is the integral from 50 to 100 of x/(24+5x^2) ?

The integral from 50 to 100 of x/(24+5x^2) is 1/10 ln(12506/3131)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 50 to 100 of x/(24+5x^2)

\int_{50}^{100} \frac{x}{24 + 5 x ^{2}} d x

\frac{1}{10} ln (\frac{12506}{3131})

Decimal

0.13848 \dots

Solution steps

\int_{50}^{100} \frac{x}{24 + 5 x ^{2}} d x

Apply u-substitution

: \int_{12524}^{50024} \frac{1}{10 u} d u

= \int_{12524}^{50024} \frac{1}{10 u} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{12524}^{50024} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} [ln ∣ u ∣]_{12524}^{50024}

Compute the boundaries:

ln (50024) - ln (12524)

= \frac{1}{10} (ln (50024) - ln (12524))

Simplify

= \frac{1}{10} ln (\frac{12506}{3131})

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

\int_{0}^{2} ∣ 2 x - 2 ∣ d x

\int_{1}^{2} 4^{3 x} d x

\int_{1}^{2} \frac{z ^{2} + 3}{z} d z

\int_{1}^{5} (\frac{2}{x}) d x

What is the integral from 50 to 100 of x/(24+5x^2) ?
The integral from 50 to 100 of x/(24+5x^2) is 1/10 ln(12506/3131)