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

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

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

\int_{1}^{5} (\frac{1}{2 x - 1}) d x

2

Solution steps

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

Apply u-substitution

: \int_{1}^{9} \frac{1}{2 u} d u

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Apply radical rule:

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

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

Compute the boundaries:

4

= \frac{1}{2} \cdot 4

Simplify

= 2

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