Optimal. Leaf size=59 \[ -\frac {1}{4} \text {RootSum}\left [2 \text {$\#$1}^6-4 \text {$\#$1}^3+1\& ,\frac {\text {$\#$1} \log \left (\sqrt [3]{x^3-2 x-1}-\text {$\#$1} x\right )-\text {$\#$1} \log (x)}{\text {$\#$1}^3-1}\& \right ] \]
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Rubi [F] time = 0.46, 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 {x (3+4 x) \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x (3+4 x) \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx &=\int \left (\frac {3 x \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6}+\frac {4 x^2 \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6}\right ) \, dx\\ &=3 \int \frac {x \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx+4 \int \frac {x^2 \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx\\ \end {align*}
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Mathematica [F] time = 0.07, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x (3+4 x) \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx \end {gather*}
Verification is not applicable to the result.
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IntegrateAlgebraic [A] time = 0.00, size = 59, normalized size = 1.00 \begin {gather*} -\frac {1}{4} \text {RootSum}\left [1-4 \text {$\#$1}^3+2 \text {$\#$1}^6\&,\frac {-\log (x) \text {$\#$1}+\log \left (\sqrt [3]{-1-2 x+x^3}-x \text {$\#$1}\right ) \text {$\#$1}}{-1+\text {$\#$1}^3}\&\right ] \end {gather*}
Antiderivative was successfully verified.
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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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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{3} - 2 \, x - 1\right )}^{\frac {1}{3}} {\left (4 \, x + 3\right )} x}{x^{6} - 8 \, x^{2} - 8 \, x - 2}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 43.21, size = 11032, normalized size = 186.98
method | result | size |
trager | \(\text {Expression too large to display}\) | \(11032\) |
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*} \int \frac {{\left (x^{3} - 2 \, x - 1\right )}^{\frac {1}{3}} {\left (4 \, x + 3\right )} x}{x^{6} - 8 \, x^{2} - 8 \, x - 2}\,{d x} \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 {x\,\left (4\,x+3\right )\,{\left (x^3-2\,x-1\right )}^{1/3}}{-x^6+8\,x^2+8\,x+2} \,d x \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 {x \sqrt [3]{\left (x + 1\right ) \left (x^{2} - x - 1\right )} \left (4 x + 3\right )}{x^{6} - 8 x^{2} - 8 x - 2}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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