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

The integral from 0 to 2 of 1/(sqrt(5x+2)) is (4sqrt(3)-2sqrt(2))/5

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

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

\frac{4 3 - 2 2}{5}

Decimal

0.81995 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{12} \frac{1}{5 u} d u

= \int_{2}^{12} \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{2}^{12} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{2}^{12}

= \frac{1}{5} [2 u^{\frac{1}{2}}]_{2}^{12}

Apply radical rule:

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

= \frac{1}{5} [2 u]_{2}^{12}

Compute the boundaries:

43 - 22

= \frac{1}{5} (43 - 22)

Simplify

= \frac{4 3 - 2 2}{5}

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What is the integral from 0 to 2 of 1/(sqrt(5x+2)) ?
The integral from 0 to 2 of 1/(sqrt(5x+2)) is (4sqrt(3)-2sqrt(2))/5