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Integrate the following functions (e^(2x) - 1)/(e^(2x) +1 |
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Answer» Solution :`(e^(2X)-1)/(e^(2x)+1) = (e^x(e^x-e^-x))/(e^x(e^x-e^+x)) = (e^x-e^-x)/(e^x+e^-x)` Let `t = e^x+e^-x`. Then dt = `(e^x-e^-x) dx` therefore `INT (e^(2x) -1)/(e^(2x)+1) dx = int(e^x-e^-x)/e^x+e^-x)dx` `int (dt)/t = LOG |t|+c` = `log|e^x+e^-x|+c` |
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