Optimal. Leaf size=22 \[ \frac {x^6}{6}-\frac {1}{4 x^4}+\frac {x^2}{2} \]
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Rubi [A] time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {x^6}{6}+\frac {x^2}{2}-\frac {1}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx &=-\frac {1}{4 x^4}+\frac {x^2}{2}+\frac {x^6}{6}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} \frac {x^6}{6}-\frac {1}{4 x^4}+\frac {x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (\frac {1}{x^5}+x+x^5\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.28, size = 17, normalized size = 0.77 \begin {gather*} \frac {2 \, x^{10} + 6 \, x^{6} - 3}{12 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.81, size = 16, normalized size = 0.73 \begin {gather*} \frac {1}{6} \, x^{6} + \frac {1}{2} \, x^{2} - \frac {1}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.77 \begin {gather*} \frac {x^{6}}{6}+\frac {x^{2}}{2}-\frac {1}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 16, normalized size = 0.73 \begin {gather*} \frac {1}{6} \, x^{6} + \frac {1}{2} \, x^{2} - \frac {1}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 17, normalized size = 0.77 \begin {gather*} \frac {2\,x^{10}+6\,x^6-3}{12\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 15, normalized size = 0.68 \begin {gather*} \frac {x^{6}}{6} + \frac {x^{2}}{2} - \frac {1}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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