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

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

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

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

\frac{x ^{4}}{4} + \frac{1}{x} - \frac{3}{5} x^{\frac{5}{3}} + C

Solution steps

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

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

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

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

= \frac{x ^{4}}{4} - (- \frac{1}{x}) - \frac{3}{5} x^{\frac{5}{3}}

Simplify

= \frac{x ^{4}}{4} + \frac{1}{x} - \frac{3}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{1}{x} - \frac{3}{5} x^{\frac{5}{3}} + C

\int 36 - (0.6 x^{2} + 2 x + 11) d x

\int_{0}^{\frac{π}{2}} 1 - 4 sin^{2} (x) d x

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

\frac{d y}{d x} = (1 + e^{x^{2}}) (5 + x)

\frac{4}{cos ( x )} + \frac{1}{tan ( x )}

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