The value of the integral $\int e^{3\mathrm{s}\mathrm{i}{\mathrm{n}}^{-1}x}\left(\frac{1}{\sqrt{1-x^2}}+e^{3\mathrm{c}\mathrm{o}{\mathrm{s}}^{-1}x}\right)dx$ is equal to
(where, $c$ is an arbitrary constant)

• A

  $\frac{e^{3\sqrt{\mathrm{s}\mathrm{i}{\mathrm{n}}^{-1}x}}}{3}+x{e}^{\frac{3\pi }{2}}+c$
• B

  $e^{\sqrt{\mathrm{s}\mathrm{i}{\mathrm{n}}^{-1}x}}+e^{\pi /2}+c$
• Correct answer
  C

  $\frac{e^{3\mathrm{s}\mathrm{i}{\mathrm{n}}^{-1}x}}{3}+x{e}^{\frac{3\pi }{2}}+c$
• D

  $e^{\frac{\pi }{2}}+e^{x\left(\frac{\pi }{2}\right)}+c$

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