What is the integral of (\sqrt[m]{e})/(m^3) ?

The integral of (\sqrt[m]{e})/(m^3) is -(3e^{1/m})/m+e^{1/m}+(2e^{1/m})/m+C

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integral of (\sqrt[m]{e})/(m^3)

- \frac{3 e ^{\frac{1}{m}}}{m} + e^{\frac{1}{m}} + \frac{2 e ^{\frac{1}{m}}}{m} + C

Solution steps

Apply Integration By Parts

= \frac{e ^{\frac{1}{m}}}{m ^{2}} - (\frac{3 e ^{\frac{1}{m}}}{m} - e^{\frac{1}{m}} + \frac{e ^{\frac{1}{m}}}{m ^{2}} - \frac{2 e ^{\frac{1}{m}}}{m})

Simplify

= - \frac{3 e ^{\frac{1}{m}}}{m} + e^{\frac{1}{m}} + \frac{2 e ^{\frac{1}{m}}}{m}

Add a constant to the solution

= - \frac{3 e ^{\frac{1}{m}}}{m} + e^{\frac{1}{m}} + \frac{2 e ^{\frac{1}{m}}}{m} + C

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What is the integral of (\sqrt[m]{e})/(m^3) ?
The integral of (\sqrt[m]{e})/(m^3) is -(3e^{1/m})/m+e^{1/m}+(2e^{1/m})/m+C