\(\int\frac{3x-2}{\sqrt{3+2x-4x^2}}dx\)
= \(\frac38\int\frac{(8x-16/3)dx}{\sqrt{3+2x-4x^2}}\)
\(=-\frac38\int\frac{(-8x+16/3)dx}{\sqrt{3+2x-4x^2}}\)
\(=-\frac38\frac{(-8x+2+10/3)dx}{\sqrt{3+2x-4x^2}}\)
\(=-\frac38\int\frac{-8x+2}{\sqrt{3+2x-4x^2}}dx\)\(-\frac38\times\frac{10}3\int\cfrac{1}{\sqrt{\frac{13}4-(2x-\frac12)^2}}dx\)
\(=-\frac38\times2\sqrt{3+2x-4x^2}-\frac52sin^{-1}(\frac{2x-1/2}{\sqrt{13}/2})+c\)
\(=-\frac34\sqrt{3+2x-4x^2}-\frac52sin^{-1}(\frac{4x-1}{\sqrt{13}})+c\)
