Optimal. Leaf size=92 \[ -\frac {2025}{704} (1-2 x)^{11/2}+\frac {1545}{32} (1-2 x)^{9/2}-\frac {159111}{448} (1-2 x)^{7/2}+\frac {121359}{80} (1-2 x)^{5/2}-\frac {832951}{192} (1-2 x)^{3/2}+\frac {381073}{32} \sqrt {1-2 x}+\frac {290521}{64 \sqrt {1-2 x}} \]
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Rubi [A] time = 0.02, antiderivative size = 92, 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} \[ -\frac {2025}{704} (1-2 x)^{11/2}+\frac {1545}{32} (1-2 x)^{9/2}-\frac {159111}{448} (1-2 x)^{7/2}+\frac {121359}{80} (1-2 x)^{5/2}-\frac {832951}{192} (1-2 x)^{3/2}+\frac {381073}{32} \sqrt {1-2 x}+\frac {290521}{64 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac {290521}{64 (1-2 x)^{3/2}}-\frac {381073}{32 \sqrt {1-2 x}}+\frac {832951}{64} \sqrt {1-2 x}-\frac {121359}{16} (1-2 x)^{3/2}+\frac {159111}{64} (1-2 x)^{5/2}-\frac {13905}{32} (1-2 x)^{7/2}+\frac {2025}{64} (1-2 x)^{9/2}\right ) \, dx\\ &=\frac {290521}{64 \sqrt {1-2 x}}+\frac {381073}{32} \sqrt {1-2 x}-\frac {832951}{192} (1-2 x)^{3/2}+\frac {121359}{80} (1-2 x)^{5/2}-\frac {159111}{448} (1-2 x)^{7/2}+\frac {1545}{32} (1-2 x)^{9/2}-\frac {2025}{704} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 43, normalized size = 0.47 \[ \frac {-212625 x^6-1146600 x^5-2899485 x^4-4819932 x^3-6831172 x^2-15214664 x+15380984}{1155 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 46, normalized size = 0.50 \[ \frac {{\left (212625 \, x^{6} + 1146600 \, x^{5} + 2899485 \, x^{4} + 4819932 \, x^{3} + 6831172 \, x^{2} + 15214664 \, x - 15380984\right )} \sqrt {-2 \, x + 1}}{1155 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 92, normalized size = 1.00 \[ \frac {2025}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {1545}{32} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {159111}{448} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {121359}{80} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {832951}{192} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {381073}{32} \, \sqrt {-2 \, x + 1} + \frac {290521}{64 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.43 \[ -\frac {212625 x^{6}+1146600 x^{5}+2899485 x^{4}+4819932 x^{3}+6831172 x^{2}+15214664 x -15380984}{1155 \sqrt {-2 x +1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 64, normalized size = 0.70 \[ -\frac {2025}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {1545}{32} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {159111}{448} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {121359}{80} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {832951}{192} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {381073}{32} \, \sqrt {-2 \, x + 1} + \frac {290521}{64 \, \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 64, normalized size = 0.70 \[ \frac {290521}{64\,\sqrt {1-2\,x}}+\frac {381073\,\sqrt {1-2\,x}}{32}-\frac {832951\,{\left (1-2\,x\right )}^{3/2}}{192}+\frac {121359\,{\left (1-2\,x\right )}^{5/2}}{80}-\frac {159111\,{\left (1-2\,x\right )}^{7/2}}{448}+\frac {1545\,{\left (1-2\,x\right )}^{9/2}}{32}-\frac {2025\,{\left (1-2\,x\right )}^{11/2}}{704} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 41.76, size = 82, normalized size = 0.89 \[ - \frac {2025 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {1545 \left (1 - 2 x\right )^{\frac {9}{2}}}{32} - \frac {159111 \left (1 - 2 x\right )^{\frac {7}{2}}}{448} + \frac {121359 \left (1 - 2 x\right )^{\frac {5}{2}}}{80} - \frac {832951 \left (1 - 2 x\right )^{\frac {3}{2}}}{192} + \frac {381073 \sqrt {1 - 2 x}}{32} + \frac {290521}{64 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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