What is the integral of (4x^{2/3}-4x^{1/5}) ?

The integral of (4x^{2/3}-4x^{1/5}) is 12/5 x^{5/3}-10/3 x^{6/5}+C

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integral of (4x^{2/3}-4x^{1/5})

\int (4 x^{\frac{2}{3}} - 4 x^{\frac{1}{5}}) d x

\frac{12}{5} x^{\frac{5}{3}} - \frac{10}{3} x^{\frac{6}{5}} + C

Solution steps

\int 4 x^{\frac{2}{3}} - 4 x^{\frac{1}{5}} 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 4 x^{\frac{2}{3}} d x - \int 4 x^{\frac{1}{5}} d x

\int 4 x^{\frac{2}{3}} d x = \frac{12}{5} x^{\frac{5}{3}}

\int 4 x^{\frac{1}{5}} d x = \frac{10}{3} x^{\frac{6}{5}}

= \frac{12}{5} x^{\frac{5}{3}} - \frac{10}{3} x^{\frac{6}{5}}

Add a constant to the solution

= \frac{12}{5} x^{\frac{5}{3}} - \frac{10}{3} x^{\frac{6}{5}} + C

What is the integral of (4x^{2/3}-4x^{1/5}) ?
The integral of (4x^{2/3}-4x^{1/5}) is 12/5 x^{5/3}-10/3 x^{6/5}+C