Optimal. Leaf size=53 \[ \frac {75}{88} (1-2 x)^{11/2}-\frac {505}{72} (1-2 x)^{9/2}+\frac {1133}{56} (1-2 x)^{7/2}-\frac {847}{40} (1-2 x)^{5/2} \]
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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} \begin {gather*} \frac {75}{88} (1-2 x)^{11/2}-\frac {505}{72} (1-2 x)^{9/2}+\frac {1133}{56} (1-2 x)^{7/2}-\frac {847}{40} (1-2 x)^{5/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x) (3+5 x)^2 \, dx &=\int \left (\frac {847}{8} (1-2 x)^{3/2}-\frac {1133}{8} (1-2 x)^{5/2}+\frac {505}{8} (1-2 x)^{7/2}-\frac {75}{8} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {847}{40} (1-2 x)^{5/2}+\frac {1133}{56} (1-2 x)^{7/2}-\frac {505}{72} (1-2 x)^{9/2}+\frac {75}{88} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.53 \begin {gather*} -\frac {(1-2 x)^{5/2} \left (23625 x^3+61775 x^2+60715 x+24617\right )}{3465} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 49, normalized size = 0.92 \begin {gather*} \frac {23625 (1-2 x)^{11/2}-194425 (1-2 x)^{9/2}+560835 (1-2 x)^{7/2}-586971 (1-2 x)^{5/2}}{27720} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.05, size = 34, normalized size = 0.64 \begin {gather*} -\frac {1}{3465} \, {\left (94500 \, x^{5} + 152600 \, x^{4} + 19385 \, x^{3} - 82617 \, x^{2} - 37753 \, x + 24617\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.00, size = 65, normalized size = 1.23 \begin {gather*} -\frac {75}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {505}{72} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {1133}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {847}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \end {gather*}
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 \begin {gather*} -\frac {\left (23625 x^{3}+61775 x^{2}+60715 x +24617\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{3465} \end {gather*}
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 \begin {gather*} \frac {75}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {505}{72} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {1133}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {847}{40} \, {\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 = 0.04, size = 37, normalized size = 0.70 \begin {gather*} \frac {1133\,{\left (1-2\,x\right )}^{7/2}}{56}-\frac {847\,{\left (1-2\,x\right )}^{5/2}}{40}-\frac {505\,{\left (1-2\,x\right )}^{9/2}}{72}+\frac {75\,{\left (1-2\,x\right )}^{11/2}}{88} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 10.19, size = 46, normalized size = 0.87 \begin {gather*} \frac {75 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} - \frac {505 \left (1 - 2 x\right )^{\frac {9}{2}}}{72} + \frac {1133 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} - \frac {847 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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