What is the integral of (sqrt(4x^2-169))/(x^2) ?

The integral of (sqrt(4x^2-169))/(x^2) is -(sqrt(4x^2-169))/x+2ln(1/13 |2x+sqrt(4x^2-169)|)+C

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integral of (sqrt(4x^2-169))/(x^2)

\int \frac{4 x ^{2} - 169}{x ^{2}} d x

- \frac{4 x ^{2} - 169}{x} + 2 ln (\frac{1}{13} 2 x + 4 x^{2} - 169) + C

Solution steps

\int \frac{4 x ^{2} - 169}{x ^{2}} d x

Apply Integration By Parts

: - \frac{4 x ^{2} - 169}{x} - \int - \frac{4}{4 x ^{2} - 169} d x

= - \frac{4 x ^{2} - 169}{x} - \int - \frac{4}{4 x ^{2} - 169} d x

\int - \frac{4}{4 x ^{2} - 169} d x = - 2 ln (\frac{1}{13} 2 x + 4 x^{2} - 169)

= - \frac{4 x ^{2} - 169}{x} - (- 2 ln (\frac{1}{13} 2 x + 4 x^{2} - 169))

Simplify

= - \frac{4 x ^{2} - 169}{x} + 2 ln (\frac{1}{13} 2 x + 4 x^{2} - 169)

Add a constant to the solution

= - \frac{4 x ^{2} - 169}{x} + 2 ln (\frac{1}{13} 2 x + 4 x^{2} - 169) + C

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What is the integral of (sqrt(4x^2-169))/(x^2) ?
The integral of (sqrt(4x^2-169))/(x^2) is -(sqrt(4x^2-169))/x+2ln(1/13 |2x+sqrt(4x^2-169)|)+C