What is the integral of (sqrt(4x^2-9))/(x^2) ?

The integral of (sqrt(4x^2-9))/(x^2) is -(sqrt(4x^2-9))/x+2ln(1/3 |2x+sqrt(4x^2-9)|)+C

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integral of (sqrt(4x^2-9))/(x^2)

\int \frac{4 x ^{2} - 9}{x ^{2}} d x

- \frac{4 x ^{2} - 9}{x} + 2 ln (\frac{1}{3} 2 x + 4 x^{2} - 9) + C

Solution steps

\int \frac{4 x ^{2} - 9}{x ^{2}} d x

Apply Integration By Parts

: - \frac{4 x ^{2} - 9}{x} - \int - \frac{4}{4 x ^{2} - 9} d x

= - \frac{4 x ^{2} - 9}{x} - \int - \frac{4}{4 x ^{2} - 9} d x

\int - \frac{4}{4 x ^{2} - 9} d x = - 2 ln (\frac{1}{3} 2 x + 4 x^{2} - 9)

= - \frac{4 x ^{2} - 9}{x} - (- 2 ln (\frac{1}{3} 2 x + 4 x^{2} - 9))

Simplify

= - \frac{4 x ^{2} - 9}{x} + 2 ln (\frac{1}{3} 2 x + 4 x^{2} - 9)

Add a constant to the solution

= - \frac{4 x ^{2} - 9}{x} + 2 ln (\frac{1}{3} 2 x + 4 x^{2} - 9) + C

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What is the integral of (sqrt(4x^2-9))/(x^2) ?
The integral of (sqrt(4x^2-9))/(x^2) is -(sqrt(4x^2-9))/x+2ln(1/3 |2x+sqrt(4x^2-9)|)+C