$\int \frac{6 x+5}{\sqrt{6+x-2 x^2}} d x=$

• Correct answer
  A

  $-3 \sqrt{6+x-2 x^2}+\frac{13}{2 \sqrt{2}} \operatorname{Sin}^{-1}\left(\frac{4 x-1}{7}\right)+c$
• B

  $-3 \sqrt{6+x-2 x^2}+\frac{13}{\sqrt{2}} \operatorname{Sinh}^{-1}\left(\frac{4 x-1}{7}\right)+c$
• C

  $-3 \sqrt{6+x-2 x^2}+\frac{13}{2 \sqrt{3}} \operatorname{Sinh}^{-1}\left(\frac{4 x+1}{7}\right)+c$
• D

  $3 \sqrt{6+x-2 x^2}-\frac{13}{2 \sqrt{2}} \operatorname{Cos}^{-1}\left(\frac{4 x-1}{7}\right)+c$

Hence, the correct answer is option: 'A'.