The value of the integral $\int {\left(\frac{\sin x}{x}\right)}^6\left(\frac{x\mathrm{c}\mathrm{o}\mathrm{s}x-\sin x}{x^2}\right)dx$ is

(where, $c$ is an arbitrary constant)

• A

  $\frac{\mathrm{s}\mathrm{i}\mathrm{n}x}{x}+c$
• B

  $\frac{\mathrm{s}\mathrm{i}\mathrm{n}x}{x^2}+c$
• C

  $\frac{\mathrm{s}\mathrm{i}{\mathrm{n}}^{7}x}{x^7}+c$
• Correct answer
  D

  $\frac{\mathrm{s}\mathrm{i}{\mathrm{n}}^{7}x}{7x^7}+c$

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