Optimal. Leaf size=46 \[ -\log \left (-x^3+x^2+\sqrt {x^6-2 x^5-x^4+4 x^3-x^2-2 x-3}+x-1\right ) \]
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Rubi [F] time = 0.31, 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 {-1-2 x+3 x^2}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {-1-2 x+3 x^2}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}} \, dx &=\int \left (-\frac {1}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}}-\frac {2 x}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}}+\frac {3 x^2}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}}\right ) \, dx\\ &=-\left (2 \int \frac {x}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}} \, dx\right )+3 \int \frac {x^2}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}} \, dx-\int \frac {1}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}} \, dx\\ \end {align*}
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Mathematica [F] time = 0.16, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-1-2 x+3 x^2}{\sqrt {-3-2 x-x^2+4 x^3-x^4-2 x^5+x^6}} \, dx \end {gather*}
Verification is not applicable to the result.
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IntegrateAlgebraic [A] time = 4.07, size = 46, normalized size = 1.00 \begin {gather*} -\log \left (-x^3+x^2+\sqrt {x^6-2 x^5-x^4+4 x^3-x^2-2 x-3}+x-1\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 44, normalized size = 0.96 \begin {gather*} \log \left (-x^{3} + x^{2} + x - \sqrt {x^{6} - 2 \, x^{5} - x^{4} + 4 \, x^{3} - x^{2} - 2 \, x - 3} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 46, normalized size = 1.00 \begin {gather*} -\log \left ({\left | -x^{3} + x^{2} + x + \sqrt {2 \, x^{3} + {\left (x^{3} - x^{2} - x\right )}^{2} - 2 \, x^{2} - 2 \, x - 3} - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 45, normalized size = 0.98 \begin {gather*} \ln \left (-x^{3}+x^{2}-\sqrt {x^{6}-2 x^{5}-x^{4}+4 x^{3}-x^{2}-2 x -3}+x -1\right ) \end {gather*}
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 {3 \, x^{2} - 2 \, x - 1}{\sqrt {x^{6} - 2 \, x^{5} - x^{4} + 4 \, x^{3} - x^{2} - 2 \, x - 3}}\,{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 {-3\,x^2+2\,x+1}{\sqrt {x^6-2\,x^5-x^4+4\,x^3-x^2-2\,x-3}} \,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 {\left (x - 1\right ) \left (3 x + 1\right )}{\sqrt {\left (x^{3} - x^{2} - x - 1\right ) \left (x^{3} - x^{2} - x + 3\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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