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

The integral from 0 to 2 of 1/(sqrt(3x+5)) is (2sqrt(11)-2sqrt(5))/3

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integral from 0 to 2 of 1/(sqrt(3x+5))

\int_{0}^{2} \frac{1}{3 x + 5} d x

\frac{2 11 - 2 5}{3}

Decimal

0.72037 \dots

Solution steps

\int_{0}^{2} \frac{1}{3 x + 5} d x

Apply u-substitution

: \int_{5}^{11} \frac{1}{3 u} d u

= \int_{5}^{11} \frac{1}{3 u} 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_{5}^{11} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{5}^{11}

= \frac{1}{3} [2 u^{\frac{1}{2}}]_{5}^{11}

Apply radical rule:

a^{\frac{1}{n}} = n a

= \frac{1}{3} [2 u]_{5}^{11}

Compute the boundaries:

211 - 25

= \frac{1}{3} (211 - 25)

Simplify

= \frac{2 11 - 2 5}{3}

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What is the integral from 0 to 2 of 1/(sqrt(3x+5)) ?
The integral from 0 to 2 of 1/(sqrt(3x+5)) is (2sqrt(11)-2sqrt(5))/3