Optimal. Leaf size=33 \[ -\log \left (-x^2+\sqrt {x^4-2 x^3+3 x^2-2 x-2}+x-1\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 37, normalized size of antiderivative = 1.12, number of steps used = 5, number of rules used = 5, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {1680, 12, 1107, 621, 206} \begin {gather*} \tanh ^{-1}\left (\frac {4 \left (x-\frac {1}{2}\right )^2+3}{\sqrt {16 \left (x-\frac {1}{2}\right )^4+24 \left (x-\frac {1}{2}\right )^2-39}}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 206
Rule 621
Rule 1107
Rule 1680
Rubi steps
\begin {align*} \int \frac {-1+2 x}{\sqrt {-2-2 x+3 x^2-2 x^3+x^4}} \, dx &=\operatorname {Subst}\left (\int \frac {8 x}{\sqrt {-39+24 x^2+16 x^4}} \, dx,x,-\frac {1}{2}+x\right )\\ &=8 \operatorname {Subst}\left (\int \frac {x}{\sqrt {-39+24 x^2+16 x^4}} \, dx,x,-\frac {1}{2}+x\right )\\ &=4 \operatorname {Subst}\left (\int \frac {1}{\sqrt {-39+24 x+16 x^2}} \, dx,x,\left (-\frac {1}{2}+x\right )^2\right )\\ &=8 \operatorname {Subst}\left (\int \frac {1}{64-x^2} \, dx,x,\frac {8 \left (3+4 \left (-\frac {1}{2}+x\right )^2\right )}{\sqrt {-39+(1-2 x)^4+24 \left (-\frac {1}{2}+x\right )^2}}\right )\\ &=\tanh ^{-1}\left (\frac {3+(-1+2 x)^2}{\sqrt {-39+6 (1-2 x)^2+(1-2 x)^4}}\right )\\ \end {align*}
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Mathematica [C] time = 3.20, size = 702, normalized size = 21.27 \begin {gather*} \frac {\sqrt {4 \sqrt {3}-3} \left (-2 x+\sqrt {4 \sqrt {3}-3}+1\right )^2 \left (\frac {-2 x-i \sqrt {3+4 \sqrt {3}}+1}{\left (\sqrt {4 \sqrt {3}-3}-i \sqrt {3+4 \sqrt {3}}\right ) \left (-2 x+\sqrt {4 \sqrt {3}-3}+1\right )}\right )^{3/2} \left (-2 x+i \sqrt {3+4 \sqrt {3}}+1\right ) \sqrt {\frac {\left (\sqrt {4 \sqrt {3}-3}-i \sqrt {3+4 \sqrt {3}}\right ) \left (2 x+\sqrt {4 \sqrt {3}-3}-1\right )}{\left (\sqrt {4 \sqrt {3}-3}+i \sqrt {3+4 \sqrt {3}}\right ) \left (-2 x+\sqrt {4 \sqrt {3}-3}+1\right )}} \left (F\left (\sin ^{-1}\left (\sqrt {\frac {\left (\sqrt {-3+4 \sqrt {3}}-i \sqrt {3+4 \sqrt {3}}\right ) \left (2 x+\sqrt {-3+4 \sqrt {3}}-1\right )}{\left (\sqrt {-3+4 \sqrt {3}}+i \sqrt {3+4 \sqrt {3}}\right ) \left (-2 x+\sqrt {-3+4 \sqrt {3}}+1\right )}}\right )|\frac {3 i+\sqrt {39}}{3 i-\sqrt {39}}\right )-2 \Pi \left (-\frac {\sqrt {-3+4 \sqrt {3}}+i \sqrt {3+4 \sqrt {3}}}{\sqrt {-3+4 \sqrt {3}}-i \sqrt {3+4 \sqrt {3}}};\sin ^{-1}\left (\sqrt {\frac {\left (\sqrt {-3+4 \sqrt {3}}-i \sqrt {3+4 \sqrt {3}}\right ) \left (2 x+\sqrt {-3+4 \sqrt {3}}-1\right )}{\left (\sqrt {-3+4 \sqrt {3}}+i \sqrt {3+4 \sqrt {3}}\right ) \left (-2 x+\sqrt {-3+4 \sqrt {3}}+1\right )}}\right )|\frac {3 i+\sqrt {39}}{3 i-\sqrt {39}}\right )\right )}{\left (-2 x-i \sqrt {3+4 \sqrt {3}}+1\right ) \sqrt {\frac {-2 x+i \sqrt {3+4 \sqrt {3}}+1}{\left (\sqrt {4 \sqrt {3}-3}+i \sqrt {3+4 \sqrt {3}}\right ) \left (-2 x+\sqrt {4 \sqrt {3}-3}+1\right )}} \sqrt {x^4-2 x^3+3 x^2-2 x-2}} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [A] time = 0.13, size = 33, normalized size = 1.00 \begin {gather*} -\log \left (-1+x-x^2+\sqrt {-2-2 x+3 x^2-2 x^3+x^4}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 31, normalized size = 0.94 \begin {gather*} \log \left (-x^{2} + x - \sqrt {x^{4} - 2 \, x^{3} + 3 \, x^{2} - 2 \, x - 2} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 34, normalized size = 1.03 \begin {gather*} -\log \left (x^{2} - x - \sqrt {{\left (x^{2} - x\right )}^{2} + 2 \, x^{2} - 2 \, x - 2} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.76, size = 34, normalized size = 1.03
method | result | size |
trager | \(-\ln \left (x^{2}-\sqrt {x^{4}-2 x^{3}+3 x^{2}-2 x -2}-x +1\right )\) | \(34\) |
default | \(-\frac {2 \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right ) \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )^{2} \sqrt {\frac {\sqrt {-3+4 \sqrt {3}}\, \left (x -\frac {1}{2}+\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \sqrt {\frac {\sqrt {-3+4 \sqrt {3}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \EllipticF \left (\sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}, \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \sqrt {-3+4 \sqrt {3}}\, \sqrt {\left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}}+\frac {4 \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right ) \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )^{2} \sqrt {\frac {\sqrt {-3+4 \sqrt {3}}\, \left (x -\frac {1}{2}+\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \sqrt {\frac {\sqrt {-3+4 \sqrt {3}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \left (\left (\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \EllipticF \left (\sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}, \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\right )-\sqrt {-3+4 \sqrt {3}}\, \EllipticPi \left (\sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}, \frac {\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}}{\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}}, \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\right )\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \sqrt {-3+4 \sqrt {3}}\, \sqrt {\left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}}\) | \(1358\) |
elliptic | \(-\frac {2 \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right ) \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )^{2} \sqrt {\frac {\sqrt {-3+4 \sqrt {3}}\, \left (x -\frac {1}{2}+\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \sqrt {\frac {\sqrt {-3+4 \sqrt {3}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \EllipticF \left (\sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}, \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \sqrt {-3+4 \sqrt {3}}\, \sqrt {\left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}}+\frac {4 \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right ) \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )^{2} \sqrt {\frac {\sqrt {-3+4 \sqrt {3}}\, \left (x -\frac {1}{2}+\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \sqrt {\frac {\sqrt {-3+4 \sqrt {3}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\, \left (\left (\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \EllipticF \left (\sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}, \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\right )-\sqrt {-3+4 \sqrt {3}}\, \EllipticPi \left (\sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}, \frac {\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}}{\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}}, \sqrt {\frac {\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {-3+4 \sqrt {3}}}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {3+4 \sqrt {3}}}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right )}}\right )\right )}{\left (\frac {i \sqrt {3+4 \sqrt {3}}}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \sqrt {-3+4 \sqrt {3}}\, \sqrt {\left (x -\frac {1}{2}+\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {3+4 \sqrt {3}}}{2}\right )}}\) | \(1358\) |
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 {2 \, x - 1}{\sqrt {x^{4} - 2 \, x^{3} + 3 \, x^{2} - 2 \, 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 = -0.03 \begin {gather*} \int \frac {2\,x-1}{\sqrt {x^4-2\,x^3+3\,x^2-2\,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 {2 x - 1}{\sqrt {x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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