What is the integral of (1-x^2-3x^2)/(x^{2/3)} ?

The integral of (1-x^2-3x^2)/(x^{2/3)} is 3x^{1/3}-12/7 x^{7/3}+C

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integral of (1-x^2-3x^2)/(x^{2/3)}

\int \frac{1 - x ^{2} - 3 x ^{2}}{x ^{\frac{2}{3}}} d x

3 x^{\frac{1}{3}} - \frac{12}{7} x^{\frac{7}{3}} + C

Solution steps

\int \frac{1 - x ^{2} - 3 x ^{2}}{x ^{\frac{2}{3}}} d x

Apply Integration By Parts

: 3 x^{\frac{1}{3}} (1 - 4 x^{2}) - \int - 24 x^{\frac{4}{3}} d x

= 3 x^{\frac{1}{3}} (1 - 4 x^{2}) - \int - 24 x^{\frac{4}{3}} d x

\int - 24 x^{\frac{4}{3}} d x = - \frac{72}{7} x^{\frac{7}{3}}

= 3 x^{\frac{1}{3}} (1 - 4 x^{2}) - (- \frac{72}{7} x^{\frac{7}{3}})

Simplify

3 x^{\frac{1}{3}} (1 - 4 x^{2}) - (- \frac{72}{7} x^{\frac{7}{3}}) : 3 x^{\frac{1}{3}} - \frac{12}{7} x^{\frac{7}{3}}

= 3 x^{\frac{1}{3}} - \frac{12}{7} x^{\frac{7}{3}}

Add a constant to the solution

= 3 x^{\frac{1}{3}} - \frac{12}{7} x^{\frac{7}{3}} + C

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What is the integral of (1-x^2-3x^2)/(x^{2/3)} ?
The integral of (1-x^2-3x^2)/(x^{2/3)} is 3x^{1/3}-12/7 x^{7/3}+C