What is the integral from 50 to 100 of x/(16+5x^2) ?

The integral from 50 to 100 of x/(16+5x^2) is 1/10 ln(4168/1043)

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integral from 50 to 100 of x/(16+5x^2)

\int_{50}^{100} \frac{x}{16 + 5 x ^{2}} d x

\frac{1}{10} ln (\frac{4168}{1043})

Decimal

0.13853 \dots

Solution steps

\int_{50}^{100} \frac{x}{16 + 5 x ^{2}} d x

Apply u-substitution

: \int_{12516}^{50016} \frac{1}{10 u} d u

= \int_{12516}^{50016} \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_{12516}^{50016} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} [ln ∣ u ∣]_{12516}^{50016}

Compute the boundaries:

ln (50016) - ln (12516)

= \frac{1}{10} (ln (50016) - ln (12516))

Simplify

= \frac{1}{10} ln (\frac{4168}{1043})

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What is the integral from 50 to 100 of x/(16+5x^2) ?
The integral from 50 to 100 of x/(16+5x^2) is 1/10 ln(4168/1043)