exponential function integral...

**thedoge** · February 4th 2007, 07:03 PM

evaluate this integral from [0,1]

int[[(e^(2x)-e^(-2x))/(e^(2x)+e^(-2x)]dx]

btw, could someone point me towards the info on how to format these correctly?

**ThePerfectHacker** · February 4th 2007, 07:10 PM

Originally Posted by thedoge

evaluate this integral from [0,1]

int[[(e^(2x)-e^(-2x))/(e^(2x)+e^(-2x)]dx]

btw, could someone point me towards the info on how to format these correctly?

This is a hyperbolic tangent, no?

$\int \tanh 2xdx=\frac{1}{2}\ln (\cosh 2x)+C$

**Soroban** · February 4th 2007, 07:11 PM

Hello, thedoge!

Evaluate: . $\int^1_0\frac{e^{2x} - e^{-2x}}{e^{2x} + e^{-2x}}\,dx$

Did you notice that the numerator is almost the derivative of the denominator?

Let $u \:=\:e^{2x} + e^{-2x}\quad\Rightarrow\quad du \:=\:\left(2e^{2x} - 2e^{-2x}\right)\,dx \:=\:2\left(e^{2x} - e^{-2x}\right)\,dx$

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