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

The integral of (x^{4/7}+5)/(x^{3/7)} is 7/8 x^{8/7}+35/4 x^{4/7}+C

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

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

\frac{7}{8} x^{\frac{8}{7}} + \frac{35}{4} x^{\frac{4}{7}} + C

Solution steps

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

Expand

\frac{x ^{\frac{4}{7}} + 5}{x ^{\frac{3}{7}}} : x^{\frac{1}{7}} + \frac{5}{x ^{\frac{3}{7}}}

= \int x^{\frac{1}{7}} + \frac{5}{x ^{\frac{3}{7}}} 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 x^{\frac{1}{7}} d x + \int \frac{5}{x ^{\frac{3}{7}}} d x

\int x^{\frac{1}{7}} d x = \frac{7}{8} x^{\frac{8}{7}}

\int \frac{5}{x ^{\frac{3}{7}}} d x = \frac{35}{4} x^{\frac{4}{7}}

= \frac{7}{8} x^{\frac{8}{7}} + \frac{35}{4} x^{\frac{4}{7}}

Add a constant to the solution

= \frac{7}{8} x^{\frac{8}{7}} + \frac{35}{4} x^{\frac{4}{7}} + C

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What is the integral of (x^{4/7}+5)/(x^{3/7)} ?
The integral of (x^{4/7}+5)/(x^{3/7)} is 7/8 x^{8/7}+35/4 x^{4/7}+C