What is the integral from 0 to 5 of 2/(sqrt(9x+8)) ?

The integral from 0 to 5 of 2/(sqrt(9x+8)) is (2(2sqrt(53)-4sqrt(2)))/9

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integral from 0 to 5 of 2/(sqrt(9x+8))

\int_{0}^{5} \frac{2}{9 x + 8} d x

\frac{2 ( 2 53 - 4 2 )}{9}

Decimal

1.97852 \dots

Solution steps

\int_{0}^{5} \frac{2}{9 x + 8} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{5} \frac{1}{9 x + 8} d x

Apply u-substitution

: \int_{8}^{53} \frac{1}{9 u} d u

= 2 \cdot \int_{8}^{53} \frac{1}{9 u} d u

Take the constant out:

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

= 2 \cdot \frac{1}{9} \cdot \int_{8}^{53} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{8}^{53}

= 2 \cdot \frac{1}{9} [2 u^{\frac{1}{2}}]_{8}^{53}

Simplify

2 \cdot \frac{1}{9} [2 u^{\frac{1}{2}}]_{8}^{53} : \frac{2}{9} [2 u]_{8}^{53}

= \frac{2}{9} [2 u]_{8}^{53}

Compute the boundaries:

253 - 42

= \frac{2}{9} (253 - 42)

Simplify

= \frac{2 ( 2 53 - 4 2 )}{9}

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What is the integral from 0 to 5 of 2/(sqrt(9x+8)) ?
The integral from 0 to 5 of 2/(sqrt(9x+8)) is (2(2sqrt(53)-4sqrt(2)))/9