$\Rightarrow \int_{1}^{e}\dfrac{1}{e^x+5}dx$
let $(e^x+5) = t\Leftrightarrow e^xdx=dt$
$\Rightarrow \int_{1}^{e}\dfrac{e^x}{(e^x+5).e^x}dx$
$\Rightarrow \int_{1}^{e}\dfrac{1}{t.(t-5)}dt$
$\Rightarrow\dfrac{1}{5}\int_{1}^{e}\left(\dfrac{1}{t-5}-\dfrac{1}{t}\right)dt$
$\Rightarrow \dfrac{1}{5}.\left\{\ln(t-5)-\ln(t)\right\}\Big|_{1}^{e} = \dfrac{1}{5}.\ln\left|\dfrac{t-5}{t}\right|\Big|_{1}^{e}=\dfrac{1}{5}\ln\left|\dfrac{e^x}{e^x+5}\right|\Big|_{1}^{e}$
$\Rightarrow \dfrac{1}{5}.\left(\ln\left|\dfrac{e^e}{e^e+5}\right|-\ln\left|\dfrac{e}{e+5}\right|\right)\Big|_{1}^{e}$
$\Rightarrow\dfrac{1}{5}.\ln\left|\dfrac{e^e.(e+5)}{(e^e+5).e}\right|$
Bài viết đã được chỉnh sửa nội dung bởi stuart clark: 25-06-2011 - 21:35