1 reply to this topic

[susubaby]

$\int \frac{e^{2x}-1}{e^{2x}+e^{x}+1}$

Edited by hoangtrong2305, 18-02-2013 - 19:59.

[duongtoi]

Ta có $\int\frac{e^{2x}-1}{e^{2x}+e^x+1}{\rm d}x=\int\frac{e^{x}-\frac{1}{e^x}}{e^{x}+1+\frac{1}{e^x}}{\rm d}x$
Đặt $e^x+\frac{1}{e^x}=t\Rightarrow {\rm d}t=\left (e^x-\frac{1}{e^x} \right ){\rm d}x$
Nên $I=\int\frac{1}{t+1}{\rm d}t=\ln|t+1|+C=\ln|e^x+e^{-x}+1|+C$

Edited by duongtoi, 19-02-2013 - 09:36.