Optimal. Leaf size=51 \[ -\frac {\tanh ^{-1}\left (\frac {6 \sqrt {6} \sqrt {x^4-3 x^3-21 x^2+83 x-60}}{29 x^2-106 x+41}\right )}{3 \sqrt {6}} \]
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Rubi [F] time = 0.32, 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 {-7+x}{(-11+5 x) \sqrt {-60+83 x-21 x^2-3 x^3+x^4}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {-7+x}{(-11+5 x) \sqrt {-60+83 x-21 x^2-3 x^3+x^4}} \, dx &=\int \left (\frac {1}{5 \sqrt {-60+83 x-21 x^2-3 x^3+x^4}}-\frac {24}{5 (-11+5 x) \sqrt {-60+83 x-21 x^2-3 x^3+x^4}}\right ) \, dx\\ &=\frac {1}{5} \int \frac {1}{\sqrt {-60+83 x-21 x^2-3 x^3+x^4}} \, dx-\frac {24}{5} \int \frac {1}{(-11+5 x) \sqrt {-60+83 x-21 x^2-3 x^3+x^4}} \, dx\\ \end {align*}
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Mathematica [C] time = 0.24, size = 131, normalized size = 2.57 \begin {gather*} -\frac {\sqrt {\frac {x-4}{x-1}} \sqrt {\frac {x-3}{x-1}} (x-1)^2 \sqrt {\frac {x+5}{x-1}} \left (3 F\left (\sin ^{-1}\left (\frac {\sqrt {\frac {x+5}{x-1}}}{\sqrt {3}}\right )|\frac {3}{4}\right )-2 \Pi \left (\frac {1}{2};\sin ^{-1}\left (\frac {\sqrt {\frac {x+5}{x-1}}}{\sqrt {3}}\right )|\frac {3}{4}\right )\right )}{3 \sqrt {6} \sqrt {x^4-3 x^3-21 x^2+83 x-60}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.13, size = 51, normalized size = 1.00 \begin {gather*} -\frac {\tanh ^{-1}\left (\frac {6 \sqrt {6} \sqrt {x^4-3 x^3-21 x^2+83 x-60}}{29 x^2-106 x+41}\right )}{3 \sqrt {6}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.44, size = 91, normalized size = 1.78 \begin {gather*} \frac {1}{36} \, \sqrt {3} \sqrt {2} \log \left (-\frac {1057 \, x^{4} - 6796 \, x^{3} - 12 \, \sqrt {3} \sqrt {2} \sqrt {x^{4} - 3 \, x^{3} - 21 \, x^{2} + 83 \, x - 60} {\left (29 \, x^{2} - 106 \, x + 41\right )} + 9078 \, x^{2} + 9236 \, x - 11279}{625 \, x^{4} - 5500 \, x^{3} + 18150 \, x^{2} - 26620 \, x + 14641}\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 - 7}{\sqrt {x^{4} - 3 \, x^{3} - 21 \, x^{2} + 83 \, x - 60} {\left (5 \, x - 11\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.03, size = 188, normalized size = 3.69 \begin {gather*} -\frac {\sqrt {\frac {5+x}{-1+x}}\, \left (-1+x \right )^{2} \sqrt {\frac {-3+x}{-1+x}}\, \sqrt {6}\, \sqrt {\frac {x -4}{-1+x}}\, \EllipticF \left (\frac {\sqrt {3}\, \sqrt {\frac {5+x}{-1+x}}}{3}, \frac {\sqrt {3}}{2}\right )}{30 \sqrt {\left (5+x \right ) \left (-1+x \right ) \left (-3+x \right ) \left (x -4\right )}}-\frac {2 \sqrt {\frac {5+x}{-1+x}}\, \left (-1+x \right )^{2} \sqrt {\frac {-3+x}{-1+x}}\, \sqrt {6}\, \sqrt {\frac {x -4}{-1+x}}\, \left (\EllipticF \left (\frac {\sqrt {3}\, \sqrt {\frac {5+x}{-1+x}}}{3}, \frac {\sqrt {3}}{2}\right )-\frac {5 \EllipticPi \left (\frac {\sqrt {3}\, \sqrt {\frac {5+x}{-1+x}}}{3}, \frac {1}{2}, \frac {\sqrt {3}}{2}\right )}{6}\right )}{15 \sqrt {\left (5+x \right ) \left (-1+x \right ) \left (-3+x \right ) \left (x -4\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 {x - 7}{\sqrt {x^{4} - 3 \, x^{3} - 21 \, x^{2} + 83 \, x - 60} {\left (5 \, x - 11\right )}}\,{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 {x-7}{\left (5\,x-11\right )\,\sqrt {x^4-3\,x^3-21\,x^2+83\,x-60}} \,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 - 7}{\sqrt {\left (x - 4\right ) \left (x - 3\right ) \left (x - 1\right ) \left (x + 5\right )} \left (5 x - 11\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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