Exercise
$\int\:\frac{x^2-3x-5}{\left(x^2-3\right)^3}dx$
Step-by-step Solution
Final answer to the exercise
$\frac{\sqrt{3}\ln\left|\frac{x+\sqrt{3}}{\sqrt{x^2-3}}\right|}{9}+\frac{-\sqrt{3}\ln\left|\frac{x+\sqrt{3}}{\sqrt{x^2-3}}\right|}{18}+\frac{-x}{6\left(x^2-3\right)}+\frac{2\sqrt{3}\ln\left|\frac{x+\sqrt{3}}{\sqrt{x^2-3}}\right|}{27}+\frac{-2\sqrt{3}\ln\left|\frac{x+\sqrt{3}}{\sqrt{x^2-3}}\right|}{27}+\frac{-2x}{9\left(x^2-3\right)}+\frac{\sqrt{3}\ln\left|\frac{x+\sqrt{3}}{\sqrt{x^2-3}}\right|}{36}+\frac{x}{12x^2-36}+\frac{x^{3}}{18\left(x^2-3\right)^{2}}+\frac{3}{4\left(x^2-3\right)^{2}}+C_0$