If $\int \frac{\sqrt{1-{\mathrm{x}}^4}}{{\mathrm{x}}^7}\mathrm{dx}=\mathrm{f}\left(\mathrm{x}\right){\left\{\sqrt{1-{\mathrm{x}}^4}\right\}}^{\mathrm{n}}+\mathrm{c}$ then ${\left(\mathrm{f}\left(\mathrm{x}\right)\right)}^{\mathrm{n}}$ is equal to

$\text{I\hspace{0.17em}=\hspace{0.17em}}\int \frac{\sqrt{{\text{1-x}}^{\text{4}}}}{{\text{x}}^{\text{7}}}\text{dx}$

$\text{I\hspace{0.17em}=\hspace{0.17em}}\int {\text{x}}^{\text{-5}}\sqrt{{\text{x}}^{\text{-4}}\text{-1}}\text{dx}$

$\text{ Put }{x}^{-4}-1=t$$\Rightarrow -4x^{-5}dx=dt$

$\text{\hspace{0.17em}=}\frac{\text{-1}}{\text{4}}\int \sqrt{\text{t}}\text{dt}$  

$\text{=\hspace{0.17em}}\frac{\text{-1}}{\text{6}}{\text{t}}^{\text{3/2}}\text{+c}$   

$\text{=\hspace{0.17em}}\frac{\text{-1}}{\text{6}}{\left({\text{x}}^{\text{-4}}\text{-1}\right)}^{\text{3/2}}\text{+c}$

$\text{=\hspace{0.17em}}\frac{\text{-1}}{{\text{6x}}^{\text{6}}}{\left({\text{1-x}}^{\text{4}}\right)}^{\text{3/2}}\text{+\hspace{0.17em}c}$

$\text{f}\left(\text{x}\right)\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{-1}}{{\text{6x}}^{\text{6}}}\text{,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}n\hspace{0.17em}=\hspace{0.17em}3}$

${\left(\text{f}\left(\text{x}\right)\right)}^{\text{n}}\text{\hspace{0.17em}=\hspace{0.17em}}{\left(\frac{\text{-1}}{{\text{6x}}^{\text{6}}}\right)}^{\text{3}}\text{=\hspace{0.17em}}\frac{\text{-1}}{{\text{216\hspace{0.17em}\hspace{0.17em}x}}^{\text{18}}}$