What is the integral from 0 to 1 of x^2\sqrt[7]{e^x} ?

The integral from 0 to 1 of x^2\sqrt[7]{e^x} is 595\sqrt[7]{e}-686

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integral from 0 to 1 of x^2\sqrt[7]{e^x}

Decimal Notation

0.37117 \dots

Solution steps

= \int_{0}^{1} e^{\frac{x}{7}} x^{2} d x

Apply Integration By Parts

: [7 e^{\frac{x}{7}} x^{2} - \int 14 e^{\frac{x}{7}} x d x]_{0}^{1}

= [7 e^{\frac{x}{7}} x^{2} - \int 14 e^{\frac{x}{7}} x d x]_{0}^{1}

\int 14 e^{\frac{x}{7}} x d x = 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}})

= [7 e^{\frac{x}{7}} x^{2} - 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}})]_{0}^{1}

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What is the integral from 0 to 1 of x^2\sqrt[7]{e^x} ?
The integral from 0 to 1 of x^2\sqrt[7]{e^x} is 595\sqrt[7]{e}-686