Optimal. Leaf size=53 \[ \frac {5}{8} (1-2 x)^{9/2}-\frac {309}{56} (1-2 x)^{7/2}+\frac {707}{40} (1-2 x)^{5/2}-\frac {539}{24} (1-2 x)^{3/2} \]
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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 {5}{8} (1-2 x)^{9/2}-\frac {309}{56} (1-2 x)^{7/2}+\frac {707}{40} (1-2 x)^{5/2}-\frac {539}{24} (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x)^2 (3+5 x) \, dx &=\int \left (\frac {539}{8} \sqrt {1-2 x}-\frac {707}{8} (1-2 x)^{3/2}+\frac {309}{8} (1-2 x)^{5/2}-\frac {45}{8} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac {539}{24} (1-2 x)^{3/2}+\frac {707}{40} (1-2 x)^{5/2}-\frac {309}{56} (1-2 x)^{7/2}+\frac {5}{8} (1-2 x)^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.53 \begin {gather*} -\frac {1}{105} (1-2 x)^{3/2} \left (525 x^3+1530 x^2+1788 x+1016\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 49, normalized size = 0.92 \begin {gather*} \frac {1}{840} \left (525 (1-2 x)^{9/2}-4635 (1-2 x)^{7/2}+14847 (1-2 x)^{5/2}-18865 (1-2 x)^{3/2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.21, size = 29, normalized size = 0.55 \begin {gather*} \frac {1}{105} \, {\left (1050 \, x^{4} + 2535 \, x^{3} + 2046 \, x^{2} + 244 \, x - 1016\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 58, normalized size = 1.09 \begin {gather*} \frac {5}{8} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {309}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {707}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {539}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \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 (525 x^{3}+1530 x^{2}+1788 x +1016\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{105} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 37, normalized size = 0.70 \begin {gather*} \frac {5}{8} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {309}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {707}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {539}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{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 {707\,{\left (1-2\,x\right )}^{5/2}}{40}-\frac {539\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {309\,{\left (1-2\,x\right )}^{7/2}}{56}+\frac {5\,{\left (1-2\,x\right )}^{9/2}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.44, size = 46, normalized size = 0.87 \begin {gather*} \frac {5 \left (1 - 2 x\right )^{\frac {9}{2}}}{8} - \frac {309 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} + \frac {707 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} - \frac {539 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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