Optimal. Leaf size=78 \[ -\frac {1}{8} \log \left (-x^8-20 x^6+128 x^5-54 x^4+1408 x^3-3124 x^2+\sqrt {x^4+10 x^2-96 x-71} \left (x^6+15 x^4-80 x^3+27 x^2-528 x+781\right )-10001\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 76, normalized size of antiderivative = 0.97, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2082} \begin {gather*} \frac {1}{8} \log \left (x^8+20 x^6-128 x^5+54 x^4-1408 x^3+3124 x^2+\sqrt {x^4+10 x^2-96 x-71} \left (x^6+15 x^4-80 x^3+27 x^2-528 x+781\right )+10001\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2082
Rubi steps
\begin {align*} \int \frac {x}{\sqrt {-71-96 x+10 x^2+x^4}} \, dx &=\frac {1}{8} \log \left (10001+3124 x^2-1408 x^3+54 x^4-128 x^5+20 x^6+x^8+\sqrt {-71-96 x+10 x^2+x^4} \left (781-528 x+27 x^2-80 x^3+15 x^4+x^6\right )\right )\\ \end {align*}
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Mathematica [C] time = 2.68, size = 1226, normalized size = 15.72
result too large to display
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [A] time = 5.17, size = 78, normalized size = 1.00 \begin {gather*} -\frac {1}{8} \log \left (-10001-3124 x^2+1408 x^3-54 x^4+128 x^5-20 x^6-x^8+\sqrt {-71-96 x+10 x^2+x^4} \left (781-528 x+27 x^2-80 x^3+15 x^4+x^6\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 72, normalized size = 0.92 \begin {gather*} \frac {1}{8} \, \log \left (x^{8} + 20 \, x^{6} - 128 \, x^{5} + 54 \, x^{4} - 1408 \, x^{3} + 3124 \, x^{2} + {\left (x^{6} + 15 \, x^{4} - 80 \, x^{3} + 27 \, x^{2} - 528 \, x + 781\right )} \sqrt {x^{4} + 10 \, x^{2} - 96 \, x - 71} + 10001\right ) \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 {x}{\sqrt {x^{4} + 10 \, x^{2} - 96 \, x - 71}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.10, size = 148, normalized size = 1.90
method | result | size |
trager | \(\frac {\ln \left (x^{8}+\sqrt {x^{4}+10 x^{2}-96 x -71}\, x^{6}+20 x^{6}+15 \sqrt {x^{4}+10 x^{2}-96 x -71}\, x^{4}-128 x^{5}-80 \sqrt {x^{4}+10 x^{2}-96 x -71}\, x^{3}+54 x^{4}+27 \sqrt {x^{4}+10 x^{2}-96 x -71}\, x^{2}-1408 x^{3}-528 x \sqrt {x^{4}+10 x^{2}-96 x -71}+3124 x^{2}+781 \sqrt {x^{4}+10 x^{2}-96 x -71}+10001\right )}{8}\) | \(148\) |
default | \(\text {Expression too large to display}\) | \(1290\) |
elliptic | \(\text {Expression too large to display}\) | \(1290\) |
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 {x}{\sqrt {x^{4} + 10 \, x^{2} - 96 \, x - 71}}\,{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 = -0.01 \begin {gather*} \int \frac {x}{\sqrt {x^4+10\,x^2-96\,x-71}} \,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 {x^{4} + 10 x^{2} - 96 x - 71}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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