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Question Number 68094 by mhmd last updated on 04/Sep/19

∫dx/(((π+e)^x^2  ))^(1/x)

$$\int{dx}/\sqrt[{{x}}]{\left(\pi+{e}\right)^{{x}^{\mathrm{2}} } }\: \\ $$

Answered by MJS last updated on 05/Sep/19

∫(dx/(((π+e)^x^2  ))^(1/x) )=∫(dx/((π+e)^x ))=−(1/((π+e)^x  ln (π+e)))+C       [∫a^x dx=(a^x /(ln a)); a=(π+e)^(−1) ]

$$\int\frac{{dx}}{\sqrt[{{x}}]{\left(\pi+\mathrm{e}\right)^{{x}^{\mathrm{2}} } }}=\int\frac{{dx}}{\left(\pi+\mathrm{e}\right)^{{x}} }=−\frac{\mathrm{1}}{\left(\pi+\mathrm{e}\right)^{{x}} \:\mathrm{ln}\:\left(\pi+\mathrm{e}\right)}+{C} \\ $$$$\:\:\:\:\:\left[\int{a}^{{x}} {dx}=\frac{{a}^{{x}} }{\mathrm{ln}\:{a}};\:{a}=\left(\pi+\mathrm{e}\right)^{−\mathrm{1}} \right] \\ $$

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