What is the integral of (5x^2+7)/(x^{4/3)} ?

The integral of (5x^2+7)/(x^{4/3)} is 3x^{5/3}-(21)/(x^{1/3)}+C

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integral of (5x^2+7)/(x^{4/3)}

\int \frac{5 x ^{2} + 7}{x ^{\frac{4}{3}}} d x

3 x^{\frac{5}{3}} - \frac{21}{x ^{\frac{1}{3}}} + C

Solution steps

\int \frac{5 x ^{2} + 7}{x ^{\frac{4}{3}}} d x

Expand

\frac{5 x ^{2} + 7}{x ^{\frac{4}{3}}} : 5 x^{\frac{2}{3}} + \frac{7}{x ^{\frac{4}{3}}}

= \int 5 x^{\frac{2}{3}} + \frac{7}{x ^{\frac{4}{3}}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 x^{\frac{2}{3}} d x + \int \frac{7}{x ^{\frac{4}{3}}} d x

\int 5 x^{\frac{2}{3}} d x = 3 x^{\frac{5}{3}}

\int \frac{7}{x ^{\frac{4}{3}}} d x = - \frac{21}{x ^{\frac{1}{3}}}

= 3 x^{\frac{5}{3}} - \frac{21}{x ^{\frac{1}{3}}}

Add a constant to the solution

= 3 x^{\frac{5}{3}} - \frac{21}{x ^{\frac{1}{3}}} + C

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What is the integral of (5x^2+7)/(x^{4/3)} ?
The integral of (5x^2+7)/(x^{4/3)} is 3x^{5/3}-(21)/(x^{1/3)}+C