What is the integral from 2 to 10 of 3/(sqrt(5x-1)) ?

The integral from 2 to 10 of 3/(sqrt(5x-1)) is 24/5

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integral from 2 to 10 of 3/(sqrt(5x-1))

\int_{2}^{10} \frac{3}{5 x - 1} d x

\frac{24}{5}

Decimal Notation

4.8

Solution steps

\int_{2}^{10} \frac{3}{5 x - 1} d x

Take the constant out:

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

= 3 \cdot \int_{2}^{10} \frac{1}{5 x - 1} d x

Apply u-substitution

: \int_{9}^{49} \frac{1}{5 u} d u

= 3 \cdot \int_{9}^{49} \frac{1}{5 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{5} \cdot \int_{9}^{49} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{9}^{49}

= 3 \cdot \frac{1}{5} [2 u^{\frac{1}{2}}]_{9}^{49}

Simplify

3 \cdot \frac{1}{5} [2 u^{\frac{1}{2}}]_{9}^{49} : \frac{3}{5} [2 u]_{9}^{49}

= \frac{3}{5} [2 u]_{9}^{49}

Compute the boundaries:

8

= \frac{3}{5} \cdot 8

Simplify

= \frac{24}{5}

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What is the integral from 2 to 10 of 3/(sqrt(5x-1)) ?
The integral from 2 to 10 of 3/(sqrt(5x-1)) is 24/5