Question

maths problem integration

Answer 1

Let
$u=1-x\\ \Rightarrow du=-dx\\ \Rightarrow \int(1-x)^{10}dx\\ =\int u^{10}(-du)\\ =-\frac{u^{11}}{11}+C\\ =-\frac{(1-x)^{11}}{11}+C\\ =\frac{(x-1)^{11}}{11}+C$