Optimal. Leaf size=47 \[ -\frac {3-x}{6 \sqrt {-x^2+6 x-7}}-\frac {3-x}{6 \left (-x^2+6 x-7\right )^{3/2}} \]
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Rubi [A] time = 0.01, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {614, 613} \[ -\frac {3-x}{6 \sqrt {-x^2+6 x-7}}-\frac {3-x}{6 \left (-x^2+6 x-7\right )^{3/2}} \]
Antiderivative was successfully verified.
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Rule 613
Rule 614
Rubi steps
\begin {align*} \int \frac {1}{\left (-7+6 x-x^2\right )^{5/2}} \, dx &=-\frac {3-x}{6 \left (-7+6 x-x^2\right )^{3/2}}+\frac {1}{3} \int \frac {1}{\left (-7+6 x-x^2\right )^{3/2}} \, dx\\ &=-\frac {3-x}{6 \left (-7+6 x-x^2\right )^{3/2}}-\frac {3-x}{6 \sqrt {-7+6 x-x^2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 0.62 \[ -\frac {(x-3) \left (x^2-6 x+6\right )}{6 \left (-x^2+6 x-7\right )^{3/2}} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.32, size = 55, normalized size = 1.17 \[ \frac {\sqrt {-x^2+6 x-7} \left (-x^3+9 x^2-24 x+18\right )}{6 \left (-x+\sqrt {2}+3\right )^2 \left (x+\sqrt {2}-3\right )^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.32, size = 47, normalized size = 1.00 \[ -\frac {{\left (x^{3} - 9 \, x^{2} + 24 \, x - 18\right )} \sqrt {-x^{2} + 6 \, x - 7}}{6 \, {\left (x^{4} - 12 \, x^{3} + 50 \, x^{2} - 84 \, x + 49\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.65, size = 35, normalized size = 0.74 \[ -\frac {{\left ({\left ({\left (x - 9\right )} x + 24\right )} x - 18\right )} \sqrt {-x^{2} + 6 \, x - 7}}{6 \, {\left (x^{2} - 6 \, x + 7\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.44, size = 28, normalized size = 0.60
method | result | size |
gosper | \(-\frac {x^{3}-9 x^{2}+24 x -18}{6 \left (-x^{2}+6 x -7\right )^{\frac {3}{2}}}\) | \(28\) |
trager | \(-\frac {\left (x^{3}-9 x^{2}+24 x -18\right ) \sqrt {-x^{2}+6 x -7}}{6 \left (x^{2}-6 x +7\right )^{2}}\) | \(38\) |
risch | \(\frac {x^{3}-9 x^{2}+24 x -18}{6 \left (x^{2}-6 x +7\right ) \sqrt {-x^{2}+6 x -7}}\) | \(38\) |
default | \(-\frac {-2 x +6}{12 \left (-x^{2}+6 x -7\right )^{\frac {3}{2}}}-\frac {-2 x +6}{12 \sqrt {-x^{2}+6 x -7}}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 59, normalized size = 1.26 \[ \frac {x}{6 \, \sqrt {-x^{2} + 6 \, x - 7}} - \frac {1}{2 \, \sqrt {-x^{2} + 6 \, x - 7}} + \frac {x}{6 \, {\left (-x^{2} + 6 \, x - 7\right )}^{\frac {3}{2}}} - \frac {1}{2 \, {\left (-x^{2} + 6 \, x - 7\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.29, size = 29, normalized size = 0.62 \[ -\frac {\left (4\,x-12\right )\,\left (8\,x^2-48\,x+48\right )}{192\,{\left (-x^2+6\,x-7\right )}^{3/2}} \]
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 \[ \int \frac {1}{\left (- x^{2} + 6 x - 7\right )^{\frac {5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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