What is the integral from 0 to 3 of (x^4)/(2x^5+pi) ?

The integral from 0 to 3 of (x^4)/(2x^5+pi) is 1/10 (ln(486+pi)-ln(pi))

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integral from 0 to 3 of (x^4)/(2x^5+pi)

\int_{0}^{3} \frac{x ^{4}}{2 x ^{5} + π} d x

\frac{1}{10} (ln (486 + π) - ln (π))

Decimal

0.50479 \dots

Solution steps

\int_{0}^{3} \frac{x ^{4}}{2 x ^{5} + π} d x

Apply u-substitution

: \int_{π}^{486 + π} \frac{1}{10 u} d u

= \int_{π}^{486 + π} \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_{π}^{486 + π} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} [ln ∣ u ∣]_{π}^{486 + π}

Compute the boundaries:

ln (486 + π) - ln (π)

= \frac{1}{10} (ln (486 + π) - ln (π))

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What is the integral from 0 to 3 of (x^4)/(2x^5+pi) ?
The integral from 0 to 3 of (x^4)/(2x^5+pi) is 1/10 (ln(486+pi)-ln(pi))