What is the integral of 7x^{2/5}-18x^{4/5} ?

The integral of 7x^{2/5}-18x^{4/5} is 5x^{7/5}-10x^{9/5}+C

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integral of 7x^{2/5}-18x^{4/5}

\int 7 x^{\frac{2}{5}} - 18 x^{\frac{4}{5}} d x

5 x^{\frac{7}{5}} - 10 x^{\frac{9}{5}} + C

Solution steps

\int 7 x^{\frac{2}{5}} - 18 x^{\frac{4}{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 7 x^{\frac{2}{5}} d x - \int 18 x^{\frac{4}{5}} d x

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

\int 18 x^{\frac{4}{5}} d x = 10 x^{\frac{9}{5}}

= 5 x^{\frac{7}{5}} - 10 x^{\frac{9}{5}}

Add a constant to the solution

= 5 x^{\frac{7}{5}} - 10 x^{\frac{9}{5}} + C

\int - \frac{x ^{2}}{x ^{2} + 1} d x

\int (5 - x^{2}) d x

\int \frac{x + sin ( x )}{cos ( x ) + 1} d x

\int e^{2 x} (e^{2 x} + 1)^{4} d x

What is the integral of 7x^{2/5}-18x^{4/5} ?
The integral of 7x^{2/5}-18x^{4/5} is 5x^{7/5}-10x^{9/5}+C