Optimal. Leaf size=59 \[ \text {RootSum}\left [1-3 \text {$\#$1}^3+\text {$\#$1}^6\& ,\frac {-\log (x) \text {$\#$1}^2+\log \left (\sqrt [3]{1+x^2+x^3}-x \text {$\#$1}\right ) \text {$\#$1}^2}{-3+2 \text {$\#$1}^3}\& \right ] \]
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Rubi [F]
time = 0.41, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\left (3+x^2\right ) \left (1+x^2+x^3\right )^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (3+x^2\right ) \left (1+x^2+x^3\right )^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx &=\int \left (\frac {3 \left (1+x^2+x^3\right )^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6}+\frac {x^2 \left (1+x^2+x^3\right )^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6}\right ) \, dx\\ &=3 \int \frac {\left (1+x^2+x^3\right )^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx+\int \frac {x^2 \left (1+x^2+x^3\right )^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.26, size = 59, normalized size = 1.00 \begin {gather*} \text {RootSum}\left [1-3 \text {$\#$1}^3+\text {$\#$1}^6\&,\frac {-\log (x) \text {$\#$1}^2+\log \left (\sqrt [3]{1+x^2+x^3}-x \text {$\#$1}\right ) \text {$\#$1}^2}{-3+2 \text {$\#$1}^3}\&\right ] \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
1.
time = 35.43, size = 9480, normalized size = 160.68
method | result | size |
trager | \(\text {Expression too large to display}\) | \(9480\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (x^{2} + 3\right ) \left (x^{3} + x^{2} + 1\right )^{\frac {2}{3}}}{x^{6} + x^{5} - x^{4} + x^{3} - 2 x^{2} - 1}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int -\frac {\left (x^2+3\right )\,{\left (x^3+x^2+1\right )}^{2/3}}{-x^6-x^5+x^4-x^3+2\,x^2+1} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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