What is the integral of (20x)/(sqrt(5x^2-6)) ?

The integral of (20x)/(sqrt(5x^2-6)) is 4sqrt(5x^2-6)+C

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integral of (20x)/(sqrt(5x^2-6))

\int \frac{20 x}{5 x ^{2} - 6} d x

4 5 x^{2} - 6 + C

Solution steps

\int \frac{20 x}{5 x ^{2} - 6} d x

Take the constant out:

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

= 20 \cdot \int \frac{x}{5 x ^{2} - 6} d x

Apply u-substitution

= 20 \cdot \int \frac{1}{10 u} d u

Take the constant out:

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

= 20 \cdot \frac{1}{10} \cdot \int \frac{1}{u} d u

Apply the Power Rule

= 20 \cdot \frac{1}{10} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 5 x^{2} - 6

= 20 \cdot \frac{1}{10} \cdot 2 (5 x^{2} - 6)^{\frac{1}{2}}

Simplify

20 \cdot \frac{1}{10} \cdot 2 (5 x^{2} - 6)^{\frac{1}{2}} : 4 5 x^{2} - 6

= 4 5 x^{2} - 6

Add a constant to the solution

= 4 5 x^{2} - 6 + C

What is the integral of (20x)/(sqrt(5x^2-6)) ?
The integral of (20x)/(sqrt(5x^2-6)) is 4sqrt(5x^2-6)+C