What is the integral from 2 to 4 of sqrt(1+81x) ?

The integral from 2 to 4 of sqrt(1+81x) is (3250sqrt(13)-326sqrt(163))/(243)

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integral from 2 to 4 of sqrt(1+81x)

\int_{2}^{4} 1 + 81 x d x

\frac{3250 13 - 326 163}{243}

Decimal Notation

31.09445 \dots

Solution steps

\int_{2}^{4} 1 + 81 x d x

Apply u-substitution

: \int_{163}^{325} \frac{u}{81} d u

= \int_{163}^{325} \frac{u}{81} d u

Take the constant out:

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

= \frac{1}{81} \cdot \int_{163}^{325} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{163}^{325}

= \frac{1}{81} [\frac{2}{3} u^{\frac{3}{2}}]_{163}^{325}

Compute the boundaries:

\frac{3250 13 - 326 163}{3}

= \frac{1}{81} \cdot \frac{3250 13 - 326 163}{3}

Simplify

= \frac{3250 13 - 326 163}{243}

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What is the integral from 2 to 4 of sqrt(1+81x) ?
The integral from 2 to 4 of sqrt(1+81x) is (3250sqrt(13)-326sqrt(163))/(243)