What is the integral of (x^{2/5}+4/x-16) ?

The integral of (x^{2/5}+4/x-16) is 5/7 x^{7/5}+4ln|x|-16x+C

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integral of (x^{2/5}+4/x-16)

\int (x^{\frac{2}{5}} + \frac{4}{x} - 16) d x

\frac{5}{7} x^{\frac{7}{5}} + 4 ln ∣ x ∣ - 16 x + C

Solution steps

\int x^{\frac{2}{5}} + \frac{4}{x} - 16 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{2}{5}} d x + \int \frac{4}{x} d x - \int 16 d x

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int 16 d x = 16 x

= \frac{5}{7} x^{\frac{7}{5}} + 4 ln ∣ x ∣ - 16 x

Add a constant to the solution

= \frac{5}{7} x^{\frac{7}{5}} + 4 ln ∣ x ∣ - 16 x + C

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What is the integral of (x^{2/5}+4/x-16) ?
The integral of (x^{2/5}+4/x-16) is 5/7 x^{7/5}+4ln|x|-16x+C