What is the integral from 0 to 1 of x^2\sqrt[6]{e^x} ?

The integral from 0 to 1 of x^2\sqrt[6]{e^x} is 366\sqrt[6]{e}-432

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of x^2\sqrt[6]{e^x}

Decimal Notation

0.37791 \dots

Solution steps

= \int_{0}^{1} e^{\frac{x}{6}} x^{2} d x

Apply Integration By Parts

: [6 e^{\frac{x}{6}} x^{2} - \int 12 e^{\frac{x}{6}} x d x]_{0}^{1}

= [6 e^{\frac{x}{6}} x^{2} - \int 12 e^{\frac{x}{6}} x d x]_{0}^{1}

\int 12 e^{\frac{x}{6}} x d x = 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}})

= [6 e^{\frac{x}{6}} x^{2} - 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}})]_{0}^{1}

Compute the boundaries:

y \cdot y^{^{'}} = \frac{5 x}{4 x ^{2} + 1}

\frac{x}{x ^{2} + 9}

\int \frac{1}{z ^{3} z ^{2} - 81} d z

\frac{\partial}{\partial x} (6 y^{8} x^{5} - 5 y^{7} x^{4})

\int \frac{( x + 2 )}{x ^{2} + 4} d x

What is the integral from 0 to 1 of x^2\sqrt[6]{e^x} ?
The integral from 0 to 1 of x^2\sqrt[6]{e^x} is 366\sqrt[6]{e}-432