Integrate : $ \int \sqrt {2x^2-5x +6 } $$dx$

Question

$(a)\;\sqrt {2} \bigg\{ \frac{1}{2} (x- \frac{5}{4} \times \sqrt {(\frac{\sqrt {23}}{4})^2 +(x-\frac{5}{4})^2 }+\large\frac{1}{2} (\frac{\sqrt {23}}{4})^2 \log \{(x -\frac{5}{4})+ \sqrt {x^2-\frac{5x}{2}+\frac{6}{2}}\} \bigg\}+c \qquad (b)\;\tan ^{-1} 3x. \log (\tan ^{-1} 3x)+c \qquad (c)\;\frac{1}{12} \{\tan ^{-1} 3x. \log (\tan ^{-1} 3x)-\tan ^{-1} 3x\} \qquad (d)\;None$