3.20.10 \(\int (x^{5/6}-x^3) \, dx\) [1910]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {6 x^{11/6}}{11}-\frac {x^4}{4} \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {6 x^{11/6}}{11}-\frac {x^4}{4} \end {gather*}

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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Mathics [A]
time = 1.68, size = 11, normalized size = 0.65 \begin {gather*} \frac {6 x^{\frac {11}{6}}}{11}-\frac {x^4}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

mathics('Integrate[x^(5/6) - x^3,x]')

[Out]

6 x ^ (11 / 6) / 11 - x ^ 4 / 4

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Maple [A]
time = 0.04, size = 12, normalized size = 0.71

method	result	size
derivativedivides	\(\frac {6 x^{\frac {11}{6}}}{11}-\frac {x^{4}}{4}\)	\(12\)
default	\(\frac {6 x^{\frac {11}{6}}}{11}-\frac {x^{4}}{4}\)	\(12\)
risch	\(\frac {6 x^{\frac {11}{6}}}{11}-\frac {x^{4}}{4}\)	\(12\)
trager	\(-\frac {\left (x^{3}+x^{2}+x +1\right ) \left (-1+x \right )}{4}+\frac {6 x^{\frac {11}{6}}}{11}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(5/6)-x^3,x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.25, size = 11, normalized size = 0.65 \begin {gather*} -\frac {1}{4} \, x^{4} + \frac {6}{11} \, x^{\frac {11}{6}} \end {gather*}

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 = 0.31, size = 11, normalized size = 0.65 \begin {gather*} -\frac {1}{4} \, x^{4} + \frac {6}{11} \, x^{\frac {11}{6}} \end {gather*}

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 = 0.03, size = 12, normalized size = 0.71 \begin {gather*} \frac {6 x^{\frac {11}{6}}}{11} - \frac {x^{4}}{4} \end {gather*}

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 = 0.00, size = 20, normalized size = 1.18 \begin {gather*} \frac {6}{11} \left (x^{\frac {1}{6}}\right )^{5} x-\frac {x^{4}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/4*x^4 + 6/11*x^(11/6)

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Mupad [B]
time = 0.03, size = 11, normalized size = 0.65 \begin {gather*} \frac {6\,x^{11/6}}{11}-\frac {x^4}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(5/6) - x^3,x)

[Out]

(6*x^(11/6))/11 - x^4/4

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