$\int x\sqrt{5x^2+50x+121}dx$

$\frac{\sqrt{\left(5\right)^{3}}\sqrt{\left(-\frac{4}{5}+\left(x+5\right)^2\right)^{3}}}{15}+\frac{20\ln\left|\frac{\sqrt{5}x+\sqrt{\left(5\right)^{3}}+\sqrt{5}\sqrt{-\frac{4}{5}+\left(x+5\right)^2}}{2}\right|}{\sqrt{5}}+\frac{\frac{-20}{\sqrt{5}}}{2}\ln\left|\sqrt{5}x+\sqrt{\left(5\right)^{3}}+\sqrt{5}\sqrt{-\frac{4}{5}+\left(x+5\right)^2}\right|+\frac{-10\sqrt{-\frac{4}{5}+\left(x+5\right)^2}\left(x+5\right)^{2}}{\frac{4\sqrt{5}}{5}\left(x+5\right)}+C_1$