Mathematics

Evaluate $$\int {\dfrac{{{e^{x - 1}} + {x^{e - 1}}}}{{{e^x} + {x^e}}}dx} $$


SOLUTION
$$\displaystyle\int \dfrac{e^{x-1}+x^{e-1}}{e^{x}+x^{e}}dx=\displaystyle\int \dfrac{\dfrac{e^{x}}{e}+x^{e-1}}{e^{x}+x^{e}}dx=\displaystyle\int \dfrac{e^{x}+e{x^{e-1}}}{e^{x}+x^{e}}\dfrac{dx}{e}=\displaystyle\int \dfrac{d(e^{x}+x^{e})}{e^{x}+x^{e}}\times \dfrac{1}{e}={\dfrac{1}{e}}{\ln(e^{x}+x^{e})}$$
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Subjective Medium Published on 17th 09, 2020
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