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

The integral of (sqrt(64x^2-49))/(x^3) is -(sqrt(64x^2-49))/(2x^2)+32/7 arcsec(8/7 x)+C

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

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

- \frac{64 x ^{2} - 49}{2 x ^{2}} + \frac{32}{7} arcsec (\frac{8}{7} x) + C

Solution steps

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

Apply Integration By Parts

: - \frac{64 x ^{2} - 49}{2 x ^{2}} - \int - \frac{32}{x 64 x ^{2} - 49} d x

= - \frac{64 x ^{2} - 49}{2 x ^{2}} - \int - \frac{32}{x 64 x ^{2} - 49} d x

\int - \frac{32}{x 64 x ^{2} - 49} d x = - \frac{32}{7} arcsec (\frac{8}{7} x)

= - \frac{64 x ^{2} - 49}{2 x ^{2}} - (- \frac{32}{7} arcsec (\frac{8}{7} x))

Simplify

= - \frac{64 x ^{2} - 49}{2 x ^{2}} + \frac{32}{7} arcsec (\frac{8}{7} x)

Add a constant to the solution

= - \frac{64 x ^{2} - 49}{2 x ^{2}} + \frac{32}{7} arcsec (\frac{8}{7} x) + C

(1 + y) d x + (1 - x) d y = 0

y^{^{'}} = y ln (\frac{1}{y})

\frac{d}{d x} (5 x - 3 x)

\int \frac{a + b x ^{5}}{6 a x + b x ^{6}} d x

\frac{d}{d x} (tan^{2} (x) sec^{2} (x))

What is the integral of (sqrt(64x^2-49))/(x^3) ?
The integral of (sqrt(64x^2-49))/(x^3) is -(sqrt(64x^2-49))/(2x^2)+32/7 arcsec(8/7 x)+C