$\int(1-x)^{23} x d x$

$\frac{x^{23}}{23}+\frac{x^{24}}{24}+c$ $\frac{(x-1)^{23}}{23}+\frac{(x-1)^{24}}{24}+C$ $\frac{(1-x)^{25}}{25}-\frac{(1-x)^{24}}{24}+c$ none of these

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

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.