What is the integral from 50 to 100 of x/(15+7x^2) ?

The integral from 50 to 100 of x/(15+7x^2) is 1/14 ln(14003/3503)

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integral from 50 to 100 of x/(15+7x^2)

\int_{50}^{100} \frac{x}{15 + 7 x ^{2}} d x

\frac{1}{14} ln (\frac{14003}{3503})

Decimal Notation

0.09897 \dots

Solution steps

\int_{50}^{100} \frac{x}{15 + 7 x ^{2}} d x

Apply u-substitution

: \int_{17515}^{70015} \frac{1}{14 u} d u

= \int_{17515}^{70015} \frac{1}{14 u} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int_{17515}^{70015} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{14} [ln ∣ u ∣]_{17515}^{70015}

Compute the boundaries:

ln (70015) - ln (17515)

= \frac{1}{14} (ln (70015) - ln (17515))

Simplify

= \frac{1}{14} ln (\frac{14003}{3503})

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What is the integral from 50 to 100 of x/(15+7x^2) ?
The integral from 50 to 100 of x/(15+7x^2) is 1/14 ln(14003/3503)