Evaluate the integral. (Use C for the constant of integration.)

Question

∫√x^2-25 / x^4 dx

Answer 1

∫ √(x²-25)/x^4 dx

∫ √(1-25/x²)/x³ dx

u = 1/x, x = 1/u, dx = -1/u² du

∫ -u√(1-25u²) du

v = √(1-25u²), dv = -25u/√(1-25u²) du

∫ (1-25u²)/25 * -25u/√(1-25u²) du

∫ v²/25 dv

v³/75 + C

(1-25u²)^(3/2)/75 + C

(1-25/x²)^(3/2)/75 + C

(x²-25)^(3/2)/(75x³) + C

Answer 2

desmos.com/calculator/mu8irlzct6