Optimal. Leaf size=40 \[ -\frac {49}{20 (-1+2 x)^{5/2}}+\frac {7}{2 (-1+2 x)^{3/2}}-\frac {9}{4 \sqrt {-1+2 x}} \]
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Rubi [A]
time = 0.01, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {45}
\begin {gather*} -\frac {9}{4 \sqrt {2 x-1}}+\frac {7}{2 (2 x-1)^{3/2}}-\frac {49}{20 (2 x-1)^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(-5+3 x)^2}{(-1+2 x)^{7/2}} \, dx &=\int \left (\frac {49}{4 (-1+2 x)^{7/2}}-\frac {21}{2 (-1+2 x)^{5/2}}+\frac {9}{4 (-1+2 x)^{3/2}}\right ) \, dx\\ &=-\frac {49}{20 (-1+2 x)^{5/2}}+\frac {7}{2 (-1+2 x)^{3/2}}-\frac {9}{4 \sqrt {-1+2 x}}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 23, normalized size = 0.58 \begin {gather*} \frac {-41+80 x-45 x^2}{5 (-1+2 x)^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 29, normalized size = 0.72
method | result | size |
gosper | \(-\frac {45 x^{2}-80 x +41}{5 \left (2 x -1\right )^{\frac {5}{2}}}\) | \(20\) |
trager | \(-\frac {45 x^{2}-80 x +41}{5 \left (2 x -1\right )^{\frac {5}{2}}}\) | \(20\) |
risch | \(-\frac {45 x^{2}-80 x +41}{5 \left (2 x -1\right )^{\frac {5}{2}}}\) | \(20\) |
derivativedivides | \(-\frac {49}{20 \left (2 x -1\right )^{\frac {5}{2}}}+\frac {7}{2 \left (2 x -1\right )^{\frac {3}{2}}}-\frac {9}{4 \sqrt {2 x -1}}\) | \(29\) |
default | \(-\frac {49}{20 \left (2 x -1\right )^{\frac {5}{2}}}+\frac {7}{2 \left (2 x -1\right )^{\frac {3}{2}}}-\frac {9}{4 \sqrt {2 x -1}}\) | \(29\) |
meijerg | \(-\frac {20 \left (-\mathrm {signum}\left (x -\frac {1}{2}\right )\right )^{\frac {7}{2}} \left (\frac {3 \sqrt {\pi }}{4}-\frac {3 \sqrt {\pi }}{4 \left (1-2 x \right )^{\frac {5}{2}}}\right )}{3 \sqrt {\pi }\, \mathrm {signum}\left (x -\frac {1}{2}\right )^{\frac {7}{2}}}-\frac {3 \left (-\mathrm {signum}\left (x -\frac {1}{2}\right )\right )^{\frac {7}{2}} \left (2 \sqrt {\pi }-\frac {\sqrt {\pi }\, \left (120 x^{2}-80 x +16\right )}{8 \left (1-2 x \right )^{\frac {5}{2}}}\right )}{5 \sqrt {\pi }\, \mathrm {signum}\left (x -\frac {1}{2}\right )^{\frac {7}{2}}}-\frac {4 \left (-\mathrm {signum}\left (x -\frac {1}{2}\right )\right )^{\frac {7}{2}} \left (\frac {\sqrt {\pi }}{2}-\frac {\sqrt {\pi }\, \left (-40 x +8\right )}{16 \left (1-2 x \right )^{\frac {5}{2}}}\right )}{\sqrt {\pi }\, \mathrm {signum}\left (x -\frac {1}{2}\right )^{\frac {7}{2}}}\) | \(128\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 23, normalized size = 0.58 \begin {gather*} -\frac {45 \, {\left (2 \, x - 1\right )}^{2} - 140 \, x + 119}{20 \, {\left (2 \, x - 1\right )}^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.17, size = 36, normalized size = 0.90 \begin {gather*} -\frac {{\left (45 \, x^{2} - 80 \, x + 41\right )} \sqrt {2 \, x - 1}}{5 \, {\left (8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 116 vs.
\(2 (34) = 68\).
time = 0.33, size = 116, normalized size = 2.90 \begin {gather*} - \frac {45 x^{2}}{20 x^{2} \sqrt {2 x - 1} - 20 x \sqrt {2 x - 1} + 5 \sqrt {2 x - 1}} + \frac {80 x}{20 x^{2} \sqrt {2 x - 1} - 20 x \sqrt {2 x - 1} + 5 \sqrt {2 x - 1}} - \frac {41}{20 x^{2} \sqrt {2 x - 1} - 20 x \sqrt {2 x - 1} + 5 \sqrt {2 x - 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.29, size = 23, normalized size = 0.58 \begin {gather*} -\frac {45 \, {\left (2 \, x - 1\right )}^{2} - 140 \, x + 119}{20 \, {\left (2 \, x - 1\right )}^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.35, size = 23, normalized size = 0.58 \begin {gather*} -\frac {\frac {9\,{\left (2\,x-1\right )}^2}{4}-7\,x+\frac {119}{20}}{{\left (2\,x-1\right )}^{5/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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