What is the integral of \sqrt[3]{8x^7} ?

The integral of \sqrt[3]{8x^7} is 3/5 x^{10/3}+C

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integral of \sqrt[3]{8x^7}

\frac{3}{5} x^{\frac{10}{3}} + C

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

assuming

x \geq 0

= 2 \cdot \int x^{\frac{7}{3}} d x

Apply the Power Rule

: \frac{3}{10} x^{\frac{10}{3}}

= 2 \cdot \frac{3}{10} x^{\frac{10}{3}}

Simplify

2 \cdot \frac{3}{10} x^{\frac{10}{3}} : \frac{3}{5} x^{\frac{10}{3}}

= \frac{3}{5} x^{\frac{10}{3}}

Add a constant to the solution

= \frac{3}{5} x^{\frac{10}{3}} + C

x \to 2 lim (x^{2} - 3 x + 5)

(\frac{4}{x})^{^{'}}

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

\int \frac{( 3 + u )}{- ( u ^{2} - 1 )} d u

y^{^{'}} = \frac{( 6 t ^{2} )}{y}

What is the integral of \sqrt[3]{8x^7} ?
The integral of \sqrt[3]{8x^7} is 3/5 x^{10/3}+C