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

ln (1 - 2 y)

\frac{\partial}{\partial x} (2 x + 2 x y)

(x + 2 y) d x + (2 x + y) d y = 0

\int (x^{2} + 3)^{5} d x

\int 42 sec^{4} (x) d x

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