Exercise
$\int_0^2\left(2x+3\right)\sqrt{4-3x+x^2}dx$
Step-by-step Solution
Final answer to the exercise
$\frac{2}{3}\sqrt{\left(\left(2-\frac{3}{2}\right)^2+\frac{7}{4}\right)^{3}}+3\cdot \left(2-\frac{3}{2}\right)\sqrt{\left(2-\frac{3}{2}\right)^2+\frac{7}{4}}+\frac{21}{4}\ln\left|\frac{2\sqrt{\left(2-\frac{3}{2}\right)^2+\frac{7}{4}}+2\cdot 2-3}{\sqrt{7}}\right|-\left(\frac{2}{3}\sqrt{\left(\left(0-\frac{3}{2}\right)^2+\frac{7}{4}\right)^{3}}+3\cdot \left(0-\frac{3}{2}\right)\sqrt{\left(0-\frac{3}{2}\right)^2+\frac{7}{4}}+\frac{21}{4}\ln\left|\frac{2\sqrt{\left(0-\frac{3}{2}\right)^2+\frac{7}{4}}+2\cdot 0-3}{\sqrt{7}}\right|\right)$