What is the integral of (sqrt(2x^2-4))/x ?

The integral of (sqrt(2x^2-4))/x is sqrt(2x^2-4)-2arctan(1/2 sqrt(2x^2-4))+C

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integral of (sqrt(2x^2-4))/x

\int \frac{2 x ^{2} - 4}{x} d x

2 x^{2} - 4 - 2 arctan (\frac{1}{2} 2 x^{2} - 4) + C

Solution steps

\int \frac{2 x ^{2} - 4}{x} d x

Apply Integration By Parts

: 2 x^{2} - 4 - \int \frac{4}{x 2 x ^{2} - 4} d x

= 2 x^{2} - 4 - \int \frac{4}{x 2 x ^{2} - 4} d x

\int \frac{4}{x 2 x ^{2} - 4} d x = 2 arctan (\frac{1}{2} 2 x^{2} - 4)

= 2 x^{2} - 4 - 2 arctan (\frac{1}{2} 2 x^{2} - 4)

Add a constant to the solution

= 2 x^{2} - 4 - 2 arctan (\frac{1}{2} 2 x^{2} - 4) + C

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What is the integral of (sqrt(2x^2-4))/x ?
The integral of (sqrt(2x^2-4))/x is sqrt(2x^2-4)-2arctan(1/2 sqrt(2x^2-4))+C