What is the integral from 0 to 1 of x^2\sqrt[3]{e^x} ?

The integral from 0 to 1 of x^2\sqrt[3]{e^x} is 39\sqrt[3]{e}-54

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integral from 0 to 1 of x^2\sqrt[3]{e^x}

Decimal Notation

0.42888 \dots

Solution steps

Apply Integration By Parts

: [3 e^{\frac{x}{3}} x^{2} - \int 6 e^{\frac{x}{3}} x d x]_{0}^{1}

= [3 e^{\frac{x}{3}} x^{2} - \int 6 e^{\frac{x}{3}} x d x]_{0}^{1}

\int 6 e^{\frac{x}{3}} x d x = 6 (3 e^{\frac{x}{3}} x - 9 e^{\frac{x}{3}})

= [3 e^{\frac{x}{3}} x^{2} - 6 (3 e^{\frac{x}{3}} x - 9 e^{\frac{x}{3}})]_{0}^{1}

Compute the boundaries:

(cos (t))^{^{'}}

\frac{d}{d x} ((x e^{2 x} + x^{3})^{6})

\int \frac{1}{2 x - x ^{2}} d x

\int_{- 1}^{0} (x^{3} - x^{2} - 2 x) d x

What is the integral from 0 to 1 of x^2\sqrt[3]{e^x} ?
The integral from 0 to 1 of x^2\sqrt[3]{e^x} is 39\sqrt[3]{e}-54