Optimal. Leaf size=25 \[ \log \left (x^2+\sqrt {x^4-2 x^3+x^2-3}-x\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps used = 5, number of rules used = 5, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.217, Rules used = {1680, 12, 1107, 621, 206} \begin {gather*} -\tanh ^{-1}\left (\frac {(1-x) x}{\sqrt {x^4-2 x^3+x^2-3}}\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 {-3+x^2-2 x^3+x^4}} \, dx &=\operatorname {Subst}\left (\int \frac {8 x}{\sqrt {-47-8 x^2+16 x^4}} \, dx,x,-\frac {1}{2}+x\right )\\ &=8 \operatorname {Subst}\left (\int \frac {x}{\sqrt {-47-8 x^2+16 x^4}} \, dx,x,-\frac {1}{2}+x\right )\\ &=4 \operatorname {Subst}\left (\int \frac {1}{\sqrt {-47-8 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 (-1+x) x}{\sqrt {-3+x^2-2 x^3+x^4}}\right )\\ &=-\tanh ^{-1}\left (\frac {(1-x) x}{\sqrt {-3+x^2-2 x^3+x^4}}\right )\\ \end {align*}
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Mathematica [C] time = 2.37, size = 728, normalized size = 29.12 \begin {gather*} \frac {\sqrt {4 \sqrt {3}-1} \left (-2 x+i \sqrt {4 \sqrt {3}-1}+1\right ) \left (-2 x+\sqrt {1+4 \sqrt {3}}+1\right ) \sqrt {\frac {\left (\sqrt {4 \sqrt {3}-1}+i \sqrt {1+4 \sqrt {3}}\right ) \left (-2 i x+\sqrt {4 \sqrt {3}-1}+i\right )}{\left (\sqrt {4 \sqrt {3}-1}-i \sqrt {1+4 \sqrt {3}}\right ) \left (2 i x+\sqrt {4 \sqrt {3}-1}-i\right )}} \sqrt {\frac {2 x+\sqrt {1+4 \sqrt {3}}-1}{\left (\sqrt {1+4 \sqrt {3}}-i \sqrt {4 \sqrt {3}-1}\right ) \left (2 i x+\sqrt {4 \sqrt {3}-1}-i\right )}} \left (F\left (\sin ^{-1}\left (\sqrt {\frac {\left (\sqrt {-1+4 \sqrt {3}}+i \sqrt {1+4 \sqrt {3}}\right ) \left (-2 i x+\sqrt {-1+4 \sqrt {3}}+i\right )}{\left (\sqrt {-1+4 \sqrt {3}}-i \sqrt {1+4 \sqrt {3}}\right ) \left (2 i x+\sqrt {-1+4 \sqrt {3}}-i\right )}}\right )|\frac {i-\sqrt {47}}{i+\sqrt {47}}\right )-2 \Pi \left (-\frac {\sqrt {-1+4 \sqrt {3}}-i \sqrt {1+4 \sqrt {3}}}{\sqrt {-1+4 \sqrt {3}}+i \sqrt {1+4 \sqrt {3}}};\sin ^{-1}\left (\sqrt {\frac {\left (\sqrt {-1+4 \sqrt {3}}+i \sqrt {1+4 \sqrt {3}}\right ) \left (-2 i x+\sqrt {-1+4 \sqrt {3}}+i\right )}{\left (\sqrt {-1+4 \sqrt {3}}-i \sqrt {1+4 \sqrt {3}}\right ) \left (2 i x+\sqrt {-1+4 \sqrt {3}}-i\right )}}\right )|\frac {i-\sqrt {47}}{i+\sqrt {47}}\right )\right )}{\left (\sqrt {4 \sqrt {3}-1}+i \sqrt {1+4 \sqrt {3}}\right ) \sqrt {\frac {-2 x+\sqrt {1+4 \sqrt {3}}+1}{\left (\sqrt {1+4 \sqrt {3}}+i \sqrt {4 \sqrt {3}-1}\right ) \left (2 i x+\sqrt {4 \sqrt {3}-1}-i\right )}} \sqrt {x^4-2 x^3+x^2-3}} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [A] time = 0.07, size = 25, normalized size = 1.00 \begin {gather*} \log \left (-x+x^2+\sqrt {-3+x^2-2 x^3+x^4}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 23, normalized size = 0.92 \begin {gather*} \log \left (x^{2} - x + \sqrt {x^{4} - 2 \, x^{3} + x^{2} - 3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 24, normalized size = 0.96 \begin {gather*} -\log \left ({\left | -x^{2} + x + \sqrt {{\left (x^{2} - x\right )}^{2} - 3} \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.74, size = 24, normalized size = 0.96
method | result | size |
trager | \(\ln \left (-x +x^{2}+\sqrt {x^{4}-2 x^{3}+x^{2}-3}\right )\) | \(24\) |
default | \(-\frac {2 \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right ) \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )^{2} \sqrt {\frac {\sqrt {1+4 \sqrt {3}}\, \left (x -\frac {1}{2}+\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \sqrt {\frac {\sqrt {1+4 \sqrt {3}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \EllipticF \left (\sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}, \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \sqrt {1+4 \sqrt {3}}\, \sqrt {\left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}}+\frac {4 \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right ) \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )^{2} \sqrt {\frac {\sqrt {1+4 \sqrt {3}}\, \left (x -\frac {1}{2}+\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \sqrt {\frac {\sqrt {1+4 \sqrt {3}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \left (\left (\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \EllipticF \left (\sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}, \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\right )-\sqrt {1+4 \sqrt {3}}\, \EllipticPi \left (\sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}, \frac {\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}}{\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}}, \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\right )\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \sqrt {1+4 \sqrt {3}}\, \sqrt {\left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}}\) | \(1358\) |
elliptic | \(-\frac {2 \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right ) \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )^{2} \sqrt {\frac {\sqrt {1+4 \sqrt {3}}\, \left (x -\frac {1}{2}+\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \sqrt {\frac {\sqrt {1+4 \sqrt {3}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \EllipticF \left (\sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}, \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \sqrt {1+4 \sqrt {3}}\, \sqrt {\left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}}+\frac {4 \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right ) \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )^{2} \sqrt {\frac {\sqrt {1+4 \sqrt {3}}\, \left (x -\frac {1}{2}+\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \sqrt {\frac {\sqrt {1+4 \sqrt {3}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\, \left (\left (\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \EllipticF \left (\sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}, \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\right )-\sqrt {1+4 \sqrt {3}}\, \EllipticPi \left (\sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}, \frac {\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}}{\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}}, \sqrt {\frac {\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {\sqrt {1+4 \sqrt {3}}}{2}-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (-\frac {i \sqrt {-1+4 \sqrt {3}}}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right )}}\right )\right )}{\left (\frac {i \sqrt {-1+4 \sqrt {3}}}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \sqrt {1+4 \sqrt {3}}\, \sqrt {\left (x -\frac {1}{2}+\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {-1+4 \sqrt {3}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {-1+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} + x^{2} - 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 = -0.04 \begin {gather*} \int \frac {2\,x-1}{\sqrt {x^4-2\,x^3+x^2-3}} \,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 {2 x - 1}{\sqrt {x^{4} - 2 x^{3} + x^{2} - 3}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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