What is the integral of (4-7x)\sqrt[3]{x} ?

The integral of (4-7x)\sqrt[3]{x} is 3x^{4/3}-3x^{7/3}+C

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integral of (4-7x)\sqrt[3]{x}

3 x^{\frac{4}{3}} - 3 x^{\frac{7}{3}} + C

Solution steps

Apply Integration By Parts

: 3 x^{\frac{4}{3}} - \frac{21}{4} x^{\frac{7}{3}} - \int - \frac{21}{4} x^{\frac{4}{3}} d x

= 3 x^{\frac{4}{3}} - \frac{21}{4} x^{\frac{7}{3}} - \int - \frac{21}{4} x^{\frac{4}{3}} d x

\int - \frac{21}{4} x^{\frac{4}{3}} d x = - \frac{9}{4} x^{\frac{7}{3}}

= 3 x^{\frac{4}{3}} - \frac{21}{4} x^{\frac{7}{3}} - (- \frac{9}{4} x^{\frac{7}{3}})

Simplify

3 x^{\frac{4}{3}} - \frac{21}{4} x^{\frac{7}{3}} - (- \frac{9}{4} x^{\frac{7}{3}}) : 3 x^{\frac{4}{3}} - 3 x^{\frac{7}{3}}

= 3 x^{\frac{4}{3}} - 3 x^{\frac{7}{3}}

Add a constant to the solution

= 3 x^{\frac{4}{3}} - 3 x^{\frac{7}{3}} + C

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What is the integral of (4-7x)\sqrt[3]{x} ?
The integral of (4-7x)\sqrt[3]{x} is 3x^{4/3}-3x^{7/3}+C