What is the integral from 0 to 1 of x^2\sqrt[5]{e^x} ?

The integral from 0 to 1 of x^2\sqrt[5]{e^x} is 205\sqrt[5]{e}-250

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integral from 0 to 1 of x^2\sqrt[5]{e^x}

Decimal Notation

0.38756 \dots

Solution steps

= \int_{0}^{1} e^{\frac{x}{5}} x^{2} d x

Apply Integration By Parts

: [5 e^{\frac{x}{5}} x^{2} - \int 10 e^{\frac{x}{5}} x d x]_{0}^{1}

= [5 e^{\frac{x}{5}} x^{2} - \int 10 e^{\frac{x}{5}} x d x]_{0}^{1}

\int 10 e^{\frac{x}{5}} x d x = 10 (5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}})

= [5 e^{\frac{x}{5}} x^{2} - 10 (5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}})]_{0}^{1}

Compute the boundaries:

\frac{\partial}{\partial x} (2 x^{3} y^{2})

x \to + 0 + lim (x^{x^{8}})

5 x y^{^{'}} - 2 y = - \frac{x ^{2}}{y ^{4}}

\int \frac{7}{4 - x ^{2}} d x

\frac{1}{( s - 1 ) ( s - 2 ) ( s - 3 )}

What is the integral from 0 to 1 of x^2\sqrt[5]{e^x} ?
The integral from 0 to 1 of x^2\sqrt[5]{e^x} is 205\sqrt[5]{e}-250