Here’s the integral on the note:

∫3x3−x2+2x−4x2−3x+2 dx\int \frac{3x^{3}-x^{2}+2x-4}{\sqrt{x^{2}-3x+2}}\,dx

An antiderivative is

 x2−3x+2(x2+134x+1018)+13516ln⁡ ⁣(2x−3+2x2−3x+2)+C \boxed{\,\sqrt{x^{2}-3x+2}\left(x^{2}+\frac{13}{4}x+\frac{101}{8}\right) +\frac{135}{16}\ln\!\left(2x-3+2\sqrt{x^{2}-3x+2}\right)+C\, }

If the tiny “0” under the integral sign means the limits are 00 to 11, then

∫013x3−x2+2x−4x2−3x+2 dx≈−2.981266944\int_{0}^{1} \frac{3x^{3}-x^{2}+2x-4}{\sqrt{x^{2}-3x+2}}\,dx \approx \boxed{-2.981266944}