Optimal. Leaf size=79 \[ \frac {1125}{352} (1-2 x)^{11/2}-\frac {4225}{96} (1-2 x)^{9/2}+\frac {28555}{112} (1-2 x)^{7/2}-\frac {64317}{80} (1-2 x)^{5/2}+\frac {48279}{32} (1-2 x)^{3/2}-\frac {65219}{32} \sqrt {1-2 x} \]
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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} \[ \frac {1125}{352} (1-2 x)^{11/2}-\frac {4225}{96} (1-2 x)^{9/2}+\frac {28555}{112} (1-2 x)^{7/2}-\frac {64317}{80} (1-2 x)^{5/2}+\frac {48279}{32} (1-2 x)^{3/2}-\frac {65219}{32} \sqrt {1-2 x} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)^3}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {65219}{32 \sqrt {1-2 x}}-\frac {144837}{32} \sqrt {1-2 x}+\frac {64317}{16} (1-2 x)^{3/2}-\frac {28555}{16} (1-2 x)^{5/2}+\frac {12675}{32} (1-2 x)^{7/2}-\frac {1125}{32} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {65219}{32} \sqrt {1-2 x}+\frac {48279}{32} (1-2 x)^{3/2}-\frac {64317}{80} (1-2 x)^{5/2}+\frac {28555}{112} (1-2 x)^{7/2}-\frac {4225}{96} (1-2 x)^{9/2}+\frac {1125}{352} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 38, normalized size = 0.48 \[ -\frac {\sqrt {1-2 x} \left (118125 x^5+518000 x^4+1024475 x^3+1252938 x^2+1167932 x+1292672\right )}{1155} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 34, normalized size = 0.43 \[ -\frac {1}{1155} \, {\left (118125 \, x^{5} + 518000 \, x^{4} + 1024475 \, x^{3} + 1252938 \, x^{2} + 1167932 \, x + 1292672\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 83, normalized size = 1.05 \[ -\frac {1125}{352} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {4225}{96} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {28555}{112} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {64317}{80} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {48279}{32} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {65219}{32} \, \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (118125 x^{5}+518000 x^{4}+1024475 x^{3}+1252938 x^{2}+1167932 x +1292672\right ) \sqrt {-2 x +1}}{1155} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 55, normalized size = 0.70 \[ \frac {1125}{352} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {4225}{96} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {28555}{112} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {64317}{80} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {48279}{32} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {65219}{32} \, \sqrt {-2 \, x + 1} \]
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 \[ \frac {48279\,{\left (1-2\,x\right )}^{3/2}}{32}-\frac {65219\,\sqrt {1-2\,x}}{32}-\frac {64317\,{\left (1-2\,x\right )}^{5/2}}{80}+\frac {28555\,{\left (1-2\,x\right )}^{7/2}}{112}-\frac {4225\,{\left (1-2\,x\right )}^{9/2}}{96}+\frac {1125\,{\left (1-2\,x\right )}^{11/2}}{352} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 59.47, size = 70, normalized size = 0.89 \[ \frac {1125 \left (1 - 2 x\right )^{\frac {11}{2}}}{352} - \frac {4225 \left (1 - 2 x\right )^{\frac {9}{2}}}{96} + \frac {28555 \left (1 - 2 x\right )^{\frac {7}{2}}}{112} - \frac {64317 \left (1 - 2 x\right )^{\frac {5}{2}}}{80} + \frac {48279 \left (1 - 2 x\right )^{\frac {3}{2}}}{32} - \frac {65219 \sqrt {1 - 2 x}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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