What is the integral from 0 to 1 of sqrt(2x+5) ?

The integral from 0 to 1 of sqrt(2x+5) is (7sqrt(7)-5sqrt(5))/3

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integral from 0 to 1 of sqrt(2x+5)

\int_{0}^{1} 2 x + 5 d x

\frac{7 7 - 5 5}{3}

Decimal

2.44663 \dots

Solution steps

\int_{0}^{1} 2 x + 5 d x

Apply u-substitution

: \int_{5}^{7} \frac{u}{2} d u

= \int_{5}^{7} \frac{u}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{5}^{7} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{7}

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{7}

Compute the boundaries:

\frac{14 7 - 10 5}{3}

= \frac{1}{2} \cdot \frac{14 7 - 10 5}{3}

Simplify

= \frac{7 7 - 5 5}{3}

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What is the integral from 0 to 1 of sqrt(2x+5) ?
The integral from 0 to 1 of sqrt(2x+5) is (7sqrt(7)-5sqrt(5))/3