What is the integral of x\sqrt[3]{x^{1/7}} ?

The integral of x\sqrt[3]{x^{1/7}} is 21/43 x^{43/21}+C

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integral of x\sqrt[3]{x^{1/7}}

\frac{21}{43} x^{\frac{43}{21}} + C

Solution steps

assuming

x \geq 0

= \int x x^{\frac{1}{21}} d x

Simplify

x x^{\frac{1}{21}} : x^{\frac{22}{21}}

= \int x^{\frac{22}{21}} d x

Apply the Power Rule

: \frac{21}{43} x^{\frac{43}{21}}

= \frac{21}{43} x^{\frac{43}{21}}

Add a constant to the solution

= \frac{21}{43} x^{\frac{43}{21}} + C

\frac{d}{d x} (6 x^{4} - 7 x^{3} + 2 x + 2)

\int \frac{z}{x ^{2} + z ^{2}} d x

\int (sin (x))^{2} (cos (x)) d x

\frac{d}{d x} (6 x^{\frac{7}{2}} + 4 x^{\frac{5}{2}} + 2 x)

What is the integral of x\sqrt[3]{x^{1/7}} ?
The integral of x\sqrt[3]{x^{1/7}} is 21/43 x^{43/21}+C