Optimal. Leaf size=33 \[ -\log \left (-x^2+\sqrt {x^4-2 x^3+5 x^2-4 x-4}+x-2\right ) \]
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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+7}{\sqrt {16 \left (x-\frac {1}{2}\right )^4+56 \left (x-\frac {1}{2}\right )^2-79}}\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 {-4-4 x+5 x^2-2 x^3+x^4}} \, dx &=\operatorname {Subst}\left (\int \frac {8 x}{\sqrt {-79+56 x^2+16 x^4}} \, dx,x,-\frac {1}{2}+x\right )\\ &=8 \operatorname {Subst}\left (\int \frac {x}{\sqrt {-79+56 x^2+16 x^4}} \, dx,x,-\frac {1}{2}+x\right )\\ &=4 \operatorname {Subst}\left (\int \frac {1}{\sqrt {-79+56 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 (7+4 \left (-\frac {1}{2}+x\right )^2\right )}{\sqrt {-79+(1-2 x)^4+56 \left (-\frac {1}{2}+x\right )^2}}\right )\\ &=\tanh ^{-1}\left (\frac {7+(-1+2 x)^2}{\sqrt {-79+14 (1-2 x)^2+(1-2 x)^4}}\right )\\ \end {align*}
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Mathematica [C] time = 3.00, size = 702, normalized size = 21.27 \begin {gather*} \frac {\sqrt {8 \sqrt {2}-7} \left (-2 x+\sqrt {8 \sqrt {2}-7}+1\right )^2 \left (\frac {-2 x-i \sqrt {7+8 \sqrt {2}}+1}{\left (\sqrt {8 \sqrt {2}-7}-i \sqrt {7+8 \sqrt {2}}\right ) \left (-2 x+\sqrt {8 \sqrt {2}-7}+1\right )}\right )^{3/2} \left (-2 x+i \sqrt {7+8 \sqrt {2}}+1\right ) \sqrt {\frac {\left (\sqrt {8 \sqrt {2}-7}-i \sqrt {7+8 \sqrt {2}}\right ) \left (2 x+\sqrt {8 \sqrt {2}-7}-1\right )}{\left (\sqrt {8 \sqrt {2}-7}+i \sqrt {7+8 \sqrt {2}}\right ) \left (-2 x+\sqrt {8 \sqrt {2}-7}+1\right )}} \left (F\left (\sin ^{-1}\left (\sqrt {\frac {\left (\sqrt {-7+8 \sqrt {2}}-i \sqrt {7+8 \sqrt {2}}\right ) \left (2 x+\sqrt {-7+8 \sqrt {2}}-1\right )}{\left (\sqrt {-7+8 \sqrt {2}}+i \sqrt {7+8 \sqrt {2}}\right ) \left (-2 x+\sqrt {-7+8 \sqrt {2}}+1\right )}}\right )|\frac {7 i+\sqrt {79}}{7 i-\sqrt {79}}\right )-2 \Pi \left (-\frac {\sqrt {-7+8 \sqrt {2}}+i \sqrt {7+8 \sqrt {2}}}{\sqrt {-7+8 \sqrt {2}}-i \sqrt {7+8 \sqrt {2}}};\sin ^{-1}\left (\sqrt {\frac {\left (\sqrt {-7+8 \sqrt {2}}-i \sqrt {7+8 \sqrt {2}}\right ) \left (2 x+\sqrt {-7+8 \sqrt {2}}-1\right )}{\left (\sqrt {-7+8 \sqrt {2}}+i \sqrt {7+8 \sqrt {2}}\right ) \left (-2 x+\sqrt {-7+8 \sqrt {2}}+1\right )}}\right )|\frac {7 i+\sqrt {79}}{7 i-\sqrt {79}}\right )\right )}{\left (-2 x-i \sqrt {7+8 \sqrt {2}}+1\right ) \sqrt {\frac {-2 x+i \sqrt {7+8 \sqrt {2}}+1}{\left (\sqrt {8 \sqrt {2}-7}+i \sqrt {7+8 \sqrt {2}}\right ) \left (-2 x+\sqrt {8 \sqrt {2}-7}+1\right )}} \sqrt {x^4-2 x^3+5 x^2-4 x-4}} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [A] time = 0.12, size = 33, normalized size = 1.00 \begin {gather*} -\log \left (-2+x-x^2+\sqrt {-4-4 x+5 x^2-2 x^3+x^4}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 29, normalized size = 0.88 \begin {gather*} \log \left (x^{2} - x + \sqrt {x^{4} - 2 \, x^{3} + 5 \, x^{2} - 4 \, x - 4} + 2\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} + 4 \, x^{2} - 4 \, x - 4} + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.76, size = 32, normalized size = 0.97
method | result | size |
trager | \(-\ln \left (-2+x -x^{2}+\sqrt {x^{4}-2 x^{3}+5 x^{2}-4 x -4}\right )\) | \(32\) |
default | \(\frac {2 i \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right ) \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )^{2} \sqrt {\frac {i \sqrt {7+8 \sqrt {2}}\, \left (x -\frac {1}{2}+\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \sqrt {\frac {i \sqrt {7+8 \sqrt {2}}\, \left (x -\frac {1}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \EllipticF \left (\sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}, \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \sqrt {7+8 \sqrt {2}}\, \sqrt {\left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}}-\frac {4 i \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right ) \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )^{2} \sqrt {\frac {i \sqrt {7+8 \sqrt {2}}\, \left (x -\frac {1}{2}+\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \sqrt {\frac {i \sqrt {7+8 \sqrt {2}}\, \left (x -\frac {1}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \left (\left (\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \EllipticF \left (\sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}, \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\right )-i \sqrt {7+8 \sqrt {2}}\, \EllipticPi \left (\sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}, \frac {\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}}{\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}}, \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\right )\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \sqrt {7+8 \sqrt {2}}\, \sqrt {\left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}}\) | \(1382\) |
elliptic | \(\frac {2 i \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right ) \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )^{2} \sqrt {\frac {i \sqrt {7+8 \sqrt {2}}\, \left (x -\frac {1}{2}+\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \sqrt {\frac {i \sqrt {7+8 \sqrt {2}}\, \left (x -\frac {1}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \EllipticF \left (\sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}, \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \sqrt {7+8 \sqrt {2}}\, \sqrt {\left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}}-\frac {4 i \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right ) \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )^{2} \sqrt {\frac {i \sqrt {7+8 \sqrt {2}}\, \left (x -\frac {1}{2}+\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \sqrt {\frac {i \sqrt {7+8 \sqrt {2}}\, \left (x -\frac {1}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\, \left (\left (\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \EllipticF \left (\sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}, \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\right )-i \sqrt {7+8 \sqrt {2}}\, \EllipticPi \left (\sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}, \frac {\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}}{\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}}, \sqrt {\frac {\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {i \sqrt {7+8 \sqrt {2}}}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (-\frac {\sqrt {-7+8 \sqrt {2}}}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right )}}\right )\right )}{\left (\frac {\sqrt {-7+8 \sqrt {2}}}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \sqrt {7+8 \sqrt {2}}\, \sqrt {\left (x -\frac {1}{2}+\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {i \sqrt {7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}+\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right ) \left (x -\frac {1}{2}-\frac {\sqrt {-7+8 \sqrt {2}}}{2}\right )}}\) | \(1382\) |
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} + 5 \, x^{2} - 4 \, x - 4}}\,{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+5\,x^2-4\,x-4}} \,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} + 5 x^{2} - 4 x - 4}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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