Exercise
$\int_1^3\left(x\sqrt{x^2+x+1}\right)dx$
Step-by-step Solution
Final answer to the exercise
$\frac{1}{3}\sqrt{\left(\left(3+\frac{1}{2}\right)^2+\frac{3}{4}\right)^{3}}-\frac{1}{4}\cdot \left(3+\frac{1}{2}\right)\sqrt{\left(3+\frac{1}{2}\right)^2+\frac{3}{4}}-\frac{3}{16}\ln\left|\frac{2\sqrt{\left(3+\frac{1}{2}\right)^2+\frac{3}{4}}+2\cdot 3+1}{\sqrt{3}}\right|-\left(\frac{1}{3}\sqrt{\left(\left(1+\frac{1}{2}\right)^2+\frac{3}{4}\right)^{3}}-\frac{1}{4}\cdot \left(1+\frac{1}{2}\right)\sqrt{\left(1+\frac{1}{2}\right)^2+\frac{3}{4}}-\frac{3}{16}\ln\left|\frac{2\sqrt{\left(1+\frac{1}{2}\right)^2+\frac{3}{4}}+2\cdot 1+1}{\sqrt{3}}\right|\right)$