Use the substitution $u={{e}^{x}}$ to show that $\displaystyle\int
olimits_{0}^{1}{\frac{{{\mathrm{

Question

Use the substitution $u={{e}^{x}}$ to show that $\displaystyle\int
olimits_{0}^{1}{\frac{{{\mathrm{e}}^{x}}-1}{{{\mathrm{e}}^{x}}+1}}\mathrm{ d}x=\displaystyle\int
olimits_{1}^{\mathrm{e}}{\frac{u-1}{u\left( u+1 ight)}}\mathrm{ d}u$. Hence, by using partial fractions, find the exact value of $\displaystyle\int
olimits_{0}^{1}{\frac{{{\mathrm{e}}^{x}}-1}{{{\mathrm{e}}^{x}}+1}}\mathrm{ d}x$. Suggest an alternative method.

Accepted Answer

−1 + 2ln((e+1)/2)

N1995 P1 Q16 [Modified]

N1995 P1 Q16 [Modified]

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