What is the integral from 1 to 2 of (15x)/(5x^2+6) ?

The integral from 1 to 2 of (15x)/(5x^2+6) is 3/2 (ln(26)-ln(11))

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integral from 1 to 2 of (15x)/(5x^2+6)

\int_{1}^{2} \frac{15 x}{5 x ^{2} + 6} d x

\frac{3}{2} (ln (26) - ln (11))

Decimal

1.29030 \dots

Solution steps

\int_{1}^{2} \frac{15 x}{5 x ^{2} + 6} d x

Take the constant out:

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

= 15 \cdot \int_{1}^{2} \frac{x}{5 x ^{2} + 6} d x

Apply u-substitution

= 15 \cdot \int_{11}^{26} \frac{1}{10 u} d u

Take the constant out:

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

= 15 \cdot \frac{1}{10} \cdot \int_{11}^{26} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 15 \cdot \frac{1}{10} [ln ∣ u ∣]_{11}^{26}

Simplify

15 \cdot \frac{1}{10} [ln ∣ u ∣]_{11}^{26} : \frac{3}{2} [ln ∣ u ∣]_{11}^{26}

= \frac{3}{2} [ln ∣ u ∣]_{11}^{26}

Compute the boundaries:

ln (26) - ln (11)

= \frac{3}{2} (ln (26) - ln (11))

What is the integral from 1 to 2 of (15x)/(5x^2+6) ?
The integral from 1 to 2 of (15x)/(5x^2+6) is 3/2 (ln(26)-ln(11))