Exercise
$\int5x^4\sqrt{x^2+5}dx$
Step-by-step Solution
Final answer to the exercise
$\frac{3125}{16}\ln\left|\sqrt{x^2+5}+x\right|+\frac{625}{16}\sqrt{x^2+5}x+\frac{3125x\sqrt{\left(x^2+5\right)^{3}}}{24\sqrt{5}\sqrt{\left(5\right)^{3}}}+\frac{625x\sqrt{\left(x^2+5\right)^{5}}}{6\sqrt{5}\sqrt{\left(5\right)^{5}}}-\frac{1875}{4}\ln\left|\frac{\sqrt{x^2+5}+x}{\sqrt{5}}\right|-\frac{375}{4}\sqrt{x^2+5}x+\frac{-625x\sqrt{\left(x^2+5\right)^{3}}}{2\sqrt{5}\sqrt{\left(5\right)^{3}}}+\frac{625}{2}\ln\left|\frac{\sqrt{x^2+5}+x}{\sqrt{5}}\right|+\frac{125}{2}x\sqrt{x^2+5}+C_1$