What is the integral of 2sqrt(x)-\sqrt[3]{x}-x^4 ?

The integral of 2sqrt(x)-\sqrt[3]{x}-x^4 is 4/3 x^{3/2}-3/4 x^{4/3}-(x^5)/5+C

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integral of 2sqrt(x)-\sqrt[3]{x}-x^4

\frac{4}{3} x^{\frac{3}{2}} - \frac{3}{4} x^{\frac{4}{3}} - \frac{x ^{5}}{5} + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int x^{4} d x = \frac{x ^{5}}{5}

= \frac{4}{3} x^{\frac{3}{2}} - \frac{3}{4} x^{\frac{4}{3}} - \frac{x ^{5}}{5}

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} - \frac{3}{4} x^{\frac{4}{3}} - \frac{x ^{5}}{5} + C

\frac{\partial}{\partial x} (- \frac{x}{x ^{2} + y ^{2}})

\int 5 cos (x) - 4 sin (x) d x

\frac{d}{d x} ((2 x + 3)^{2})

f (x) = a^{4} + cos^{4} (x)

What is the integral of 2sqrt(x)-\sqrt[3]{x}-x^4 ?
The integral of 2sqrt(x)-\sqrt[3]{x}-x^4 is 4/3 x^{3/2}-3/4 x^{4/3}-(x^5)/5+C