Integrate the function $\sqrt{1+3x-x^2}$

Question

$\begin{array}{1 1}\large \frac{(2x-3)(\sqrt{1+3x-x^2})}{4} +\frac{13 }{8}\sin^{-1}(\large \frac{2x-3}{\sqrt {13}})+c \\\large \frac{(2x-3)(\sqrt{1+3x-x^2})}{4} -\frac{13 }{8}\cos^{-1}(\large \frac{2x-3}{\sqrt {13}})+c \\ \large \frac{(3x+2)(\sqrt{1+3x-x^2})}{4} +\frac{13 }{8}\cos^{-1}(\large \frac{2x-3}{\sqrt {13}})+c \\ \large \frac{(3-2x)(\sqrt{1+3x-x^2})}{4} -\frac{13 }{8}\sin^{-1}(\large \frac{2x-3}{\sqrt {13}})+c \end{array}$