ính tích phân I = intlimits_1^3 {x{{left( {x - 1} ight)}^{1000}}dx}

Đặt $x - 1 = t \Rightarrow dx = dt,$ khi $x = 1 \Rightarrow t = 0;{\rm{ }}x = 3 \Rightarrow t = 2$

Khi đó: $I = \int\limits_0^2 {(t + 1){t^{1000}}dt} = \int\limits_0^2 {\left( {{t^{1001}} + {t^{1000}}} \right)dt}$

$\begin{array}{l} = \left( {\frac{{{t^{1002}}}}{{1002}} + \frac{{{t^{1001}}}}{{1001}}} \right)\left| \begin{array}{l} ^2\\ _0 \end{array} \right. = = \frac{{{2^{1002}}}}{{1002}} + \frac{{{2^{1001}}}}{{1001}}\\ = {2^{1001}}\left( {\frac{2}{{1002}} + \frac{1}{{1001}}} \right) = \frac{{{{1502.2}^{1001}}}}{{501501}}. \end{array}$