Đáp án:
\[ - \frac{1}{7}{\left( {x - 3} \right)^7} - \frac{1}{2}{\left( {x - 3} \right)^6}\]
Giải thích các bước giải:
\(\begin{array}{l}
\int {x{{\left( {3 - x} \right)}^5}dx} \\
= \int {\left[ {\left( {x - 3} \right){{\left( {3 - x} \right)}^5} + 3.{{\left( {3 - x} \right)}^5}} \right]dx} \\
= - \int {{{\left( {x - 3} \right)}^6}dx} + 3.\int {{{\left( {3 - x} \right)}^5}dx} \\
= - \int {{{\left( {x - 3} \right)}^6}d\left( {x - 3} \right)} - 3.\int {{{\left( {3 - x} \right)}^5}d\left( {3 - x} \right)} \\
= - \frac{{{{\left( {x - 3} \right)}^7}}}{7} - 3.\frac{{{{\left( {3 - x} \right)}^6}}}{6}\\
= - \frac{1}{7}{\left( {x - 3} \right)^7} - \frac{1}{2}{\left( {x - 3} \right)^6}
\end{array}\)
