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

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

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

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

3

Solution steps

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

Apply u-substitution

= \int_{1}^{49} \frac{1}{4 u} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{1}^{49} \frac{1}{u} d u

Apply the Power Rule

= \frac{1}{4} [2 u^{\frac{1}{2}}]_{1}^{49}

Apply radical rule:

= \frac{1}{4} [2 u]_{1}^{49}

Compute the boundaries:

12

= \frac{1}{4} \cdot 12

Simplify

= 3

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