b: \(A=\int20\cdot x\cdot e^{5x}=20\cdot\int x\cdot e^{5x}\)
Đặt \(\left\{{}\begin{matrix}u=x\\dv=e^{5x}.dx\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}du=dx\\v=\dfrac{1}{5}\cdot e^{5x}\end{matrix}\right.\)
\(I=x\cdot\dfrac{1}{5}\cdot e^{5x}-\int\dfrac{1}{5}\cdot e^{5x}.dx\)
\(=\dfrac{1}{5}\cdot x\cdot e^{5x}-\dfrac{1}{5}\cdot\dfrac{1}{5}\cdot e^{5x}=e^{5x}\left(\dfrac{1}{5}x-\dfrac{1}{25}\right)\)
=>\(A=20\cdot e^{5x}\left(\dfrac{1}{5}x-\dfrac{1}{25}\right)\)
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