Solve ∫ x^2-24x-45/x^3-3x wrt x

$$\int \frac { x ^ { 2 } - 24 x - 45 } { x ^ { 3 } - 3 x } d x$$

Evaluate

$$-7\ln(|x^{2}-3|)+15\ln(|x|)-4\sqrt{3}\ln(\frac{|x-\sqrt{3}|}{|x+\sqrt{3}|})+С$$

Differentiate w.r.t. x

$$\frac{|x-\sqrt{3}|x^{3}-4\sqrt{3}sign(x-\sqrt{3})x^{4}+4\sqrt{3}|x-\sqrt{3}|x^{3}-12sign(x-\sqrt{3})x^{3}+12\sqrt{3}sign(x-\sqrt{3})x^{2}+\sqrt{3}|x-\sqrt{3}|x^{2}-12\sqrt{3}x|x-\sqrt{3}|+36xsign(x-\sqrt{3})-45x|x-\sqrt{3}|-45\sqrt{3}|x-\sqrt{3}|}{x|x-\sqrt{3}|\left(x+\sqrt{3}\right)\left(x^{2}-3\right)}$$