What is the integral from 2 to 6 of 1/(sqrt(5x+6)) ?

The integral from 2 to 6 of 1/(sqrt(5x+6)) is 4/5

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integral from 2 to 6 of 1/(sqrt(5x+6))

\int_{2}^{6} \frac{1}{5 x + 6} d x

\frac{4}{5}

Decimal

0.8

Solution steps

\int_{2}^{6} \frac{1}{5 x + 6} d x

Apply u-substitution

: \int_{16}^{36} \frac{1}{5 u} d u

= \int_{16}^{36} \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_{16}^{36} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{16}^{36}

= \frac{1}{5} [2 u^{\frac{1}{2}}]_{16}^{36}

Apply radical rule:

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

= \frac{1}{5} [2 u]_{16}^{36}

Compute the boundaries:

4

= \frac{1}{5} \cdot 4

Simplify

= \frac{4}{5}

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What is the integral from 2 to 6 of 1/(sqrt(5x+6)) ?
The integral from 2 to 6 of 1/(sqrt(5x+6)) is 4/5