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

The integral of (sqrt(2x^2-5))/x is sqrt(2x^2-5)-sqrt(5)arctan(sqrt(1/5 (2x^2-5)))+C

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

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

2 x^{2} - 5 - 5 arctan (\frac{1}{5} (2 x^{2} - 5)) + C

Solution steps

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

Apply Integration By Parts

: 2 x^{2} - 5 - \int \frac{5}{x 2 x ^{2} - 5} d x

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

\int \frac{5}{x 2 x ^{2} - 5} d x = 5 arctan (\frac{1}{5} (2 x^{2} - 5))

= 2 x^{2} - 5 - 5 arctan (\frac{1}{5} (2 x^{2} - 5))

Add a constant to the solution

= 2 x^{2} - 5 - 5 arctan (\frac{1}{5} (2 x^{2} - 5)) + C

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What is the integral of (sqrt(2x^2-5))/x ?
The integral of (sqrt(2x^2-5))/x is sqrt(2x^2-5)-sqrt(5)arctan(sqrt(1/5 (2x^2-5)))+C