Optimal. Leaf size=53 \[ \frac {125}{104} (1-2 x)^{13/2}-\frac {75}{8} (1-2 x)^{11/2}+\frac {605}{24} (1-2 x)^{9/2}-\frac {1331}{56} (1-2 x)^{7/2} \]
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Rubi [A] time = 0.01, antiderivative size = 53, 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 = {43} \[ \frac {125}{104} (1-2 x)^{13/2}-\frac {75}{8} (1-2 x)^{11/2}+\frac {605}{24} (1-2 x)^{9/2}-\frac {1331}{56} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (3+5 x)^3 \, dx &=\int \left (\frac {1331}{8} (1-2 x)^{5/2}-\frac {1815}{8} (1-2 x)^{7/2}+\frac {825}{8} (1-2 x)^{9/2}-\frac {125}{8} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac {1331}{56} (1-2 x)^{7/2}+\frac {605}{24} (1-2 x)^{9/2}-\frac {75}{8} (1-2 x)^{11/2}+\frac {125}{104} (1-2 x)^{13/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.53 \[ -\frac {1}{273} (1-2 x)^{7/2} \left (2625 x^3+6300 x^2+5495 x+1838\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 39, normalized size = 0.74 \[ \frac {1}{273} \, {\left (21000 \, x^{6} + 18900 \, x^{5} - 15890 \, x^{4} - 16061 \, x^{3} + 4614 \, x^{2} + 5533 \, x - 1838\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 65, normalized size = 1.23 \[ \frac {125}{104} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {75}{8} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {605}{24} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {1331}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.47 \[ -\frac {\left (2625 x^{3}+6300 x^{2}+5495 x +1838\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{273} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 37, normalized size = 0.70 \[ \frac {125}{104} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {75}{8} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {605}{24} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {1331}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.70 \[ \frac {605\,{\left (1-2\,x\right )}^{9/2}}{24}-\frac {1331\,{\left (1-2\,x\right )}^{7/2}}{56}-\frac {75\,{\left (1-2\,x\right )}^{11/2}}{8}+\frac {125\,{\left (1-2\,x\right )}^{13/2}}{104} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.95, size = 100, normalized size = 1.89 \[ \frac {1000 x^{6} \sqrt {1 - 2 x}}{13} + \frac {900 x^{5} \sqrt {1 - 2 x}}{13} - \frac {2270 x^{4} \sqrt {1 - 2 x}}{39} - \frac {16061 x^{3} \sqrt {1 - 2 x}}{273} + \frac {1538 x^{2} \sqrt {1 - 2 x}}{91} + \frac {5533 x \sqrt {1 - 2 x}}{273} - \frac {1838 \sqrt {1 - 2 x}}{273} \]
Verification of antiderivative is not currently implemented for this CAS.
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