Mathematics - Definite Integration Question with Solution | TestHub

$1={\int }_0^1(1-x_1^4{)}^7-\underset{\pi }{1}dx$

$$\begin{array}{rl}& ={\left[x(1-x^4{)}^7\right]}_0^1+7\times 4{\int }_0^{1}x(1-x^4{)}^6{x}^{3}dx\\ & =-28{\int }_0^1(1-x^4{)}^{6}dx+28{\int }_0^1(1-x^4{)}^{6}dx\\ & =-28I+28{\int }_0^1(1-x^4{)}^{6}dx\\ & 29I-28{\int }_0^1(1-x^4)dx\\ & \frac{29{\int }_0^1(1-x^4{)}^{7}dx}{4{\int }_0^1(1-x^4{)}^{7}dx}=7\end{array}$$