Optimal. Leaf size=53 \[ \frac {75}{104} (1-2 x)^{13/2}-\frac {505}{88} (1-2 x)^{11/2}+\frac {1133}{72} (1-2 x)^{9/2}-\frac {121}{8} (1-2 x)^{7/2} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ \frac {75}{104} (1-2 x)^{13/2}-\frac {505}{88} (1-2 x)^{11/2}+\frac {1133}{72} (1-2 x)^{9/2}-\frac {121}{8} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x) (3+5 x)^2 \, dx &=\int \left (\frac {847}{8} (1-2 x)^{5/2}-\frac {1133}{8} (1-2 x)^{7/2}+\frac {505}{8} (1-2 x)^{9/2}-\frac {75}{8} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac {121}{8} (1-2 x)^{7/2}+\frac {1133}{72} (1-2 x)^{9/2}-\frac {505}{88} (1-2 x)^{11/2}+\frac {75}{104} (1-2 x)^{13/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.53 \[ -\frac {(1-2 x)^{7/2} \left (7425 x^3+18405 x^2+16531 x+5671\right )}{1287} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 39, normalized size = 0.74 \[ \frac {1}{1287} \, {\left (59400 \, x^{6} + 58140 \, x^{5} - 44062 \, x^{4} - 49999 \, x^{3} + 12729 \, x^{2} + 17495 \, x - 5671\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 65, normalized size = 1.23 \[ \frac {75}{104} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {505}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {1133}{72} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {121}{8} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (7425 x^{3}+18405 x^{2}+16531 x +5671\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{1287} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 37, normalized size = 0.70 \[ \frac {75}{104} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {505}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {1133}{72} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {121}{8} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 37, normalized size = 0.70 \[ \frac {1133\,{\left (1-2\,x\right )}^{9/2}}{72}-\frac {121\,{\left (1-2\,x\right )}^{7/2}}{8}-\frac {505\,{\left (1-2\,x\right )}^{11/2}}{88}+\frac {75\,{\left (1-2\,x\right )}^{13/2}}{104} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.08, size = 100, normalized size = 1.89 \[ \frac {600 x^{6} \sqrt {1 - 2 x}}{13} + \frac {6460 x^{5} \sqrt {1 - 2 x}}{143} - \frac {44062 x^{4} \sqrt {1 - 2 x}}{1287} - \frac {49999 x^{3} \sqrt {1 - 2 x}}{1287} + \frac {4243 x^{2} \sqrt {1 - 2 x}}{429} + \frac {17495 x \sqrt {1 - 2 x}}{1287} - \frac {5671 \sqrt {1 - 2 x}}{1287} \]
Verification of antiderivative is not currently implemented for this CAS.
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