Optimal. Leaf size=79 \[ \frac {675}{352} (1-2 x)^{11/2}-\frac {855}{32} (1-2 x)^{9/2}+\frac {17541}{112} (1-2 x)^{7/2}-\frac {39977}{80} (1-2 x)^{5/2}+\frac {91091}{96} (1-2 x)^{3/2}-\frac {41503}{32} \sqrt {1-2 x} \]
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Rubi [A] time = 0.01, antiderivative size = 79, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {88} \[ \frac {675}{352} (1-2 x)^{11/2}-\frac {855}{32} (1-2 x)^{9/2}+\frac {17541}{112} (1-2 x)^{7/2}-\frac {39977}{80} (1-2 x)^{5/2}+\frac {91091}{96} (1-2 x)^{3/2}-\frac {41503}{32} \sqrt {1-2 x} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)^2}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {41503}{32 \sqrt {1-2 x}}-\frac {91091}{32} \sqrt {1-2 x}+\frac {39977}{16} (1-2 x)^{3/2}-\frac {17541}{16} (1-2 x)^{5/2}+\frac {7695}{32} (1-2 x)^{7/2}-\frac {675}{32} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {41503}{32} \sqrt {1-2 x}+\frac {91091}{96} (1-2 x)^{3/2}-\frac {39977}{80} (1-2 x)^{5/2}+\frac {17541}{112} (1-2 x)^{7/2}-\frac {855}{32} (1-2 x)^{9/2}+\frac {675}{352} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 38, normalized size = 0.48 \[ -\frac {\sqrt {1-2 x} \left (70875 x^5+316575 x^4+636795 x^3+790023 x^2+743822 x+826982\right )}{1155} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 34, normalized size = 0.43 \[ -\frac {1}{1155} \, {\left (70875 \, x^{5} + 316575 \, x^{4} + 636795 \, x^{3} + 790023 \, x^{2} + 743822 \, x + 826982\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 83, normalized size = 1.05 \[ -\frac {675}{352} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {855}{32} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {17541}{112} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {39977}{80} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {91091}{96} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {41503}{32} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.44 \[ -\frac {\left (70875 x^{5}+316575 x^{4}+636795 x^{3}+790023 x^{2}+743822 x +826982\right ) \sqrt {-2 x +1}}{1155} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 55, normalized size = 0.70 \[ \frac {675}{352} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {855}{32} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {17541}{112} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {39977}{80} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {91091}{96} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {41503}{32} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 55, normalized size = 0.70 \[ \frac {91091\,{\left (1-2\,x\right )}^{3/2}}{96}-\frac {41503\,\sqrt {1-2\,x}}{32}-\frac {39977\,{\left (1-2\,x\right )}^{5/2}}{80}+\frac {17541\,{\left (1-2\,x\right )}^{7/2}}{112}-\frac {855\,{\left (1-2\,x\right )}^{9/2}}{32}+\frac {675\,{\left (1-2\,x\right )}^{11/2}}{352} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 72.28, size = 70, normalized size = 0.89 \[ \frac {675 \left (1 - 2 x\right )^{\frac {11}{2}}}{352} - \frac {855 \left (1 - 2 x\right )^{\frac {9}{2}}}{32} + \frac {17541 \left (1 - 2 x\right )^{\frac {7}{2}}}{112} - \frac {39977 \left (1 - 2 x\right )^{\frac {5}{2}}}{80} + \frac {91091 \left (1 - 2 x\right )^{\frac {3}{2}}}{96} - \frac {41503 \sqrt {1 - 2 x}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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