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

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

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

\int \frac{( 4 x + 7 )}{x ^{2} - 5 x + 8} d x

\int 1 + x + x^{2} + x^{3} d x

\int x e^{- \frac{x ^{2}}{4}} d x

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

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