Mathematics - Indefinite Integration Question with Solution | TestHub

$I_{10}=\int {\left(1-x^5\right)}^{10}\mathrm{dx}$

$=x{\left(1-x^5\right)}^{10}-\int x10{\left(1-x^5\right)}^9\left(-5x^4\right)dx$

$=\mathrm{x}{\left(1-{\mathrm{x}}^5\right)}^{10}+50{\mathrm{I}}_9-50{\mathrm{I}}_{10}$

$\Rightarrow {\mathrm{I}}_{10}=\frac{\mathrm{x}{\left(1-{\mathrm{x}}^5\right)}^{10}}{51}+\frac{50}{51}{\mathrm{I}}_9$

$\Rightarrow \mathrm{n}=50;\mathrm{m}=51$