∫(1-x)^23 x d x

Put (1 –x) = t

–dx = dt

$\int-d t t^{23}(1-t)=\int\left(t^{24}-t^{23}\right) d t$

$=\frac{t^{25}}{25}-\frac{t^{24}}{24}+c=\frac{(1-x)^{25}}{25}-\frac{(1-x)^{24}}{24}+c$

Hence (3) is the correct answer.