What is the integral of \sqrt[3]{xsqrt(2/x)} ?

The integral of \sqrt[3]{xsqrt(2/x)} is x\sqrt[3]{sqrt(2)sqrt(x)}-1/14 (sqrt(2/x)x)^{7/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of \sqrt[3]{xsqrt(2/x)}

\int 3 x \frac{2}{x} d x

x 3 2 x - \frac{1}{14} (\frac{2}{x} x)^{\frac{7}{3}} + C

Solution steps

\int 3 x \frac{2}{x} d x

Apply u-substitution

: \int u 3 u d u

= \int u 3 u d u

Apply Integration By Parts

: \frac{1}{2} u^{2} 3 u - \int \frac{1}{6} u^{\frac{4}{3}} d u

= \frac{1}{2} u^{2} 3 u - \int \frac{1}{6} u^{\frac{4}{3}} d u

\int \frac{1}{6} u^{\frac{4}{3}} d u = \frac{1}{14} u^{\frac{7}{3}}

= \frac{1}{2} u^{2} 3 u - \frac{1}{14} u^{\frac{7}{3}}

Substitute back

u = x \frac{2}{x}

= \frac{1}{2} (x \frac{2}{x})^{2} 3 x \frac{2}{x} - \frac{1}{14} (x \frac{2}{x})^{\frac{7}{3}}

\frac{1}{2} (x \frac{2}{x})^{2} 3 x \frac{2}{x} = x 3 2 x

= x 3 2 x - \frac{1}{14} (\frac{2}{x} x)^{\frac{7}{3}}

Add a constant to the solution

= x 3 2 x - \frac{1}{14} (\frac{2}{x} x)^{\frac{7}{3}} + C

\frac{\partial}{\partial y} (40 x + 840 - 40 y)

\int 2 x + e^{x} d x

\int (ln (x)) d x

\int \frac{16}{1 - cos ( 8 x )} d x

e^{- t + 1}

What is the integral of \sqrt[3]{xsqrt(2/x)} ?
The integral of \sqrt[3]{xsqrt(2/x)} is x\sqrt[3]{sqrt(2)sqrt(x)}-1/14 (sqrt(2/x)x)^{7/3}+C