3.1910 \(\int (x^{5/6}-x^3) \, dx\)

Optimal. Leaf size=17 \[ \frac{6 x^{11/6}}{11}-\frac{x^4}{4} \]

[Out]

(6*x^(11/6))/11 - x^4/4

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Rubi [A]  time = 0.0018104, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{6 x^{11/6}}{11}-\frac{x^4}{4} \]

Antiderivative was successfully verified.

[In]

Int[x^(5/6) - x^3,x]

[Out]

(6*x^(11/6))/11 - x^4/4

Rubi steps

\begin{align*} \int \left (x^{5/6}-x^3\right ) \, dx &=\frac{6 x^{11/6}}{11}-\frac{x^4}{4}\\ \end{align*}

Mathematica [A]  time = 0.0019205, size = 17, normalized size = 1. \[ \frac{6 x^{11/6}}{11}-\frac{x^4}{4} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(5/6) - x^3,x]

[Out]

(6*x^(11/6))/11 - x^4/4

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Maple [A]  time = 0., size = 12, normalized size = 0.7 \begin{align*}{\frac{6}{11}{x}^{{\frac{11}{6}}}}-{\frac{{x}^{4}}{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(5/6)-x^3,x)

[Out]

6/11*x^(11/6)-1/4*x^4

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Maxima [A]  time = 0.969834, size = 15, normalized size = 0.88 \begin{align*} -\frac{1}{4} \, x^{4} + \frac{6}{11} \, x^{\frac{11}{6}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(5/6)-x^3,x, algorithm="maxima")

[Out]

-1/4*x^4 + 6/11*x^(11/6)

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Fricas [A]  time = 1.89175, size = 35, normalized size = 2.06 \begin{align*} -\frac{1}{4} \, x^{4} + \frac{6}{11} \, x^{\frac{11}{6}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(5/6)-x^3,x, algorithm="fricas")

[Out]

-1/4*x^4 + 6/11*x^(11/6)

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Sympy [A]  time = 0.055255, size = 12, normalized size = 0.71 \begin{align*} \frac{6 x^{\frac{11}{6}}}{11} - \frac{x^{4}}{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**(5/6)-x**3,x)

[Out]

6*x**(11/6)/11 - x**4/4

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Giac [A]  time = 1.05014, size = 15, normalized size = 0.88 \begin{align*} -\frac{1}{4} \, x^{4} + \frac{6}{11} \, x^{\frac{11}{6}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(5/6)-x^3,x, algorithm="giac")

[Out]

-1/4*x^4 + 6/11*x^(11/6)