What is the integral from 3 to 9 of sqrt(1+3x) ?

The integral from 3 to 9 of sqrt(1+3x) is (112sqrt(7)-20sqrt(10))/9

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integral from 3 to 9 of sqrt(1+3x)

\int_{3}^{9} 1 + 3 x d x

\frac{112 7 - 20 10}{9}

Decimal Notation

25.89762 \dots

Solution steps

\int_{3}^{9} 1 + 3 x d x

Apply u-substitution

: \int_{10}^{28} \frac{u}{3} d u

= \int_{10}^{28} \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{10}^{28} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{10}^{28}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{10}^{28}

Compute the boundaries:

\frac{112 7 - 20 10}{3}

= \frac{1}{3} \cdot \frac{112 7 - 20 10}{3}

Simplify

= \frac{112 7 - 20 10}{9}

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What is the integral from 3 to 9 of sqrt(1+3x) ?
The integral from 3 to 9 of sqrt(1+3x) is (112sqrt(7)-20sqrt(10))/9