$I_n=\underset{0}{\overset{\pi /2}{\int }}{x}^n.\cos xdx$ then the value of $I_9+72I_7=$

$$\begin{gathered} {\mathrm{I}}_{\mathrm{n}}={\int }_0^{\mathrm{\pi }/2} {\mathrm{x}}^{\mathrm{n}}. \cos \mathrm{x} \mathrm{dx} \\ ={\mathrm{x}}^{\mathrm{n}}(\mathrm{Sm} \mathrm{x}){]}_0^{\mathrm{\pi }/2}-{\int }_0^{\mathrm{\pi }/2}\mathrm{n}.{\mathrm{x}}^{\mathrm{n}-1}(\mathrm{Sm} \mathrm{x}) \mathrm{dx} \\ ={\left(\frac{\mathrm{\pi }}{2}\right)}^{\mathrm{n}}-\mathrm{n} {\int }_0^{\mathrm{\pi }/2}{\mathrm{x}}^{\mathrm{n}-1}.\mathrm{Sm} \mathrm{x} \mathrm{dx} \\ ={\left(\frac{\mathrm{\pi }}{2}\right)}^{\mathrm{n}}-\mathrm{n}{\left[\left({\mathrm{x}}^{\mathrm{n}-1}\right).\left(-(\cos \mathrm{x})\right)\right]}_0^{\mathrm{\pi }/2}-{\int }_0^{\mathrm{\pi }/2}(\mathrm{n}-1){\mathrm{x}}^{\mathrm{n}-2}(-(\cos \mathrm{x}\left)\mathrm{dx}\right) \\ ={\left(\frac{\mathrm{\pi }}{2}\right)}^{\mathrm{n}}-\mathrm{n}\left[0+(\mathrm{n}-1) {\int }_0^{\mathrm{\pi }/2}{\mathrm{x}}^{\mathrm{n}-2} \cos \mathrm{x} \mathrm{dx}\right] \\ ={\left(\frac{\mathrm{\pi }}{2}\right)}^{\mathrm{n}}-\mathrm{n}(\mathrm{n}-1) {\mathrm{I}}_{\mathrm{n}-2} \\ {\mathrm{I}}_{\mathrm{n}}+\mathrm{n}(\mathrm{n}-1) {\mathrm{I}}_{\mathrm{n}-2}={\left(\frac{\mathrm{\pi }}{2}\right)}^{\mathrm{n}} \\ \mathrm{n}=9 \Rightarrow {\mathrm{I}}_9+72 {\mathrm{I}}_7=={\left(\frac{\mathrm{\pi }}{2}\right)}^9 \end{gathered}$$