What is the integral of (sqrt(49x^2-64))/(x^3) ?

The integral of (sqrt(49x^2-64))/(x^3) is -(sqrt(49x^2-64))/(2x^2)+49/16 arcsec(7/8 x)+C

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integral of (sqrt(49x^2-64))/(x^3)

\int \frac{49 x ^{2} - 64}{x ^{3}} d x

- \frac{49 x ^{2} - 64}{2 x ^{2}} + \frac{49}{16} arcsec (\frac{7}{8} x) + C

Solution steps

\int \frac{49 x ^{2} - 64}{x ^{3}} d x

Apply Integration By Parts

: - \frac{49 x ^{2} - 64}{2 x ^{2}} - \int - \frac{49}{2 x 49 x ^{2} - 64} d x

= - \frac{49 x ^{2} - 64}{2 x ^{2}} - \int - \frac{49}{2 x 49 x ^{2} - 64} d x

\int - \frac{49}{2 x 49 x ^{2} - 64} d x = - \frac{49}{16} arcsec (\frac{7}{8} x)

= - \frac{49 x ^{2} - 64}{2 x ^{2}} - (- \frac{49}{16} arcsec (\frac{7}{8} x))

Simplify

= - \frac{49 x ^{2} - 64}{2 x ^{2}} + \frac{49}{16} arcsec (\frac{7}{8} x)

Add a constant to the solution

= - \frac{49 x ^{2} - 64}{2 x ^{2}} + \frac{49}{16} arcsec (\frac{7}{8} x) + C

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What is the integral of (sqrt(49x^2-64))/(x^3) ?
The integral of (sqrt(49x^2-64))/(x^3) is -(sqrt(49x^2-64))/(2x^2)+49/16 arcsec(7/8 x)+C