Giải thích các bước giải:
\(\begin{array}{l}
1)I = \int\limits_0^{\dfrac{\pi }{2}} {{{\sin }^3}xd\left( {\sin x} \right)} = \left. {\dfrac{{{{\sin }^4}x}}{4}} \right|_0^{\dfrac{\pi }{2}} = \dfrac{1}{4}\\
2)\left\{ \begin{array}{l}
2x - 1 = u\\
{e^x}dx = dv
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
dx = \dfrac{{du}}{2}\\
v = {e^x}
\end{array} \right.\\
I = \left. {\left( {2x - 1} \right).{e^x}} \right|_0^1 - \int\limits_0^1 {\dfrac{{{e^x}}}{2}dx} \\
= e - 1 - \left. {\dfrac{{{e^x}}}{2}} \right|_0^1 = \dfrac{e}{2} - \dfrac{1}{2}\\
3)I = \left. {\left( {{x^2} + 3x} \right)} \right|_1^2 = {2^2} + 3.2 - \left( {1 + 3.1} \right) = 6
\end{array}\)