$\int \sqrt{e^{x}+e^{-x}-2}dx$
$\int \sqrt{e^{x}+e^{-x}-2}dx$
Started By Mr0, 17-06-2012 - 15:32
#1
Posted 17-06-2012 - 15:32
#2
Posted 17-06-2012 - 15:38
$\int \sqrt{e^{x}+e^{-x}-2}dx$
Hướng dẫn:
Ta có: \[\int {\sqrt {{e^x} + {e^{ - x}} - 2} dx = } \int {\sqrt {\frac{{{e^{2x}} - 2{e^x} + 1}}{{{e^x}}}} dx = \int {\sqrt {\frac{{{{\left( {{e^x} - 1} \right)}^2}}}{{{e^x}}}} } dx = \int {\frac{{\left| {{e^x} - 1} \right|}}{{\sqrt {{e^x}} }}dx} } \]
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