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

The integral of (sqrt(x^2-49))/(x^3) is -(sqrt(x^2-49))/(2x^2)+1/14 arcsec(1/7 x)+C

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

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

- \frac{x ^{2} - 49}{2 x ^{2}} + \frac{1}{14} arcsec (\frac{1}{7} x) + C

Solution steps

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

Apply Integration By Parts

: - \frac{x ^{2} - 49}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 49} d x

= - \frac{x ^{2} - 49}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 49} d x

\int - \frac{1}{2 x x ^{2} - 49} d x = - \frac{1}{14} arcsec (\frac{1}{7} x)

= - \frac{x ^{2} - 49}{2 x ^{2}} - (- \frac{1}{14} arcsec (\frac{1}{7} x))

Simplify

= - \frac{x ^{2} - 49}{2 x ^{2}} + \frac{1}{14} arcsec (\frac{1}{7} x)

Add a constant to the solution

= - \frac{x ^{2} - 49}{2 x ^{2}} + \frac{1}{14} arcsec (\frac{1}{7} x) + C

\frac{\partial}{\partial x} (4 x y e^{x})

x \to 2 lim (3 x^{4} + 2 x^{2} - x + 1)

x \to - 8 lim (x^{3})

y^{^{''}} + 25 y = e^{- t}

k = 1 \sum \infty \frac{1}{k ( k + 1 )}

What is the integral of (sqrt(x^2-49))/(x^3) ?
The integral of (sqrt(x^2-49))/(x^3) is -(sqrt(x^2-49))/(2x^2)+1/14 arcsec(1/7 x)+C