Optimal. Leaf size=92 \[ -\frac {2025 (1-2 x)^{19/2}}{1216}+\frac {13905}{544} (1-2 x)^{17/2}-\frac {53037}{320} (1-2 x)^{15/2}+\frac {121359}{208} (1-2 x)^{13/2}-\frac {832951}{704} (1-2 x)^{11/2}+\frac {381073}{288} (1-2 x)^{9/2}-\frac {41503}{64} (1-2 x)^{7/2} \]
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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} \[ -\frac {2025 (1-2 x)^{19/2}}{1216}+\frac {13905}{544} (1-2 x)^{17/2}-\frac {53037}{320} (1-2 x)^{15/2}+\frac {121359}{208} (1-2 x)^{13/2}-\frac {832951}{704} (1-2 x)^{11/2}+\frac {381073}{288} (1-2 x)^{9/2}-\frac {41503}{64} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac {290521}{64} (1-2 x)^{5/2}-\frac {381073}{32} (1-2 x)^{7/2}+\frac {832951}{64} (1-2 x)^{9/2}-\frac {121359}{16} (1-2 x)^{11/2}+\frac {159111}{64} (1-2 x)^{13/2}-\frac {13905}{32} (1-2 x)^{15/2}+\frac {2025}{64} (1-2 x)^{17/2}\right ) \, dx\\ &=-\frac {41503}{64} (1-2 x)^{7/2}+\frac {381073}{288} (1-2 x)^{9/2}-\frac {832951}{704} (1-2 x)^{11/2}+\frac {121359}{208} (1-2 x)^{13/2}-\frac {53037}{320} (1-2 x)^{15/2}+\frac {13905}{544} (1-2 x)^{17/2}-\frac {2025 (1-2 x)^{19/2}}{1216}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 43, normalized size = 0.47 \[ -\frac {(1-2 x)^{7/2} \left (221524875 x^6+1035520200 x^5+2092364703 x^4+2374399764 x^3+1634664492 x^2+673648856 x+138993368\right )}{2078505} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.96, size = 54, normalized size = 0.59 \[ \frac {1}{2078505} \, {\left (1772199000 \, x^{9} + 5625863100 \, x^{8} + 5641824474 \, x^{7} - 121581999 \, x^{6} - 3896813214 \, x^{5} - 2072749175 \, x^{4} + 461747860 \, x^{3} + 739308228 \, x^{2} + 160311352 \, x - 138993368\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.87, size = 113, normalized size = 1.23 \[ \frac {2025}{1216} \, {\left (2 \, x - 1\right )}^{9} \sqrt {-2 \, x + 1} + \frac {13905}{544} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} + \frac {53037}{320} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {121359}{208} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {832951}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {381073}{288} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {41503}{64} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (221524875 x^{6}+1035520200 x^{5}+2092364703 x^{4}+2374399764 x^{3}+1634664492 x^{2}+673648856 x +138993368\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{2078505} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 64, normalized size = 0.70 \[ -\frac {2025}{1216} \, {\left (-2 \, x + 1\right )}^{\frac {19}{2}} + \frac {13905}{544} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} - \frac {53037}{320} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {121359}{208} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {832951}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {381073}{288} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {41503}{64} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
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 \[ \frac {381073\,{\left (1-2\,x\right )}^{9/2}}{288}-\frac {41503\,{\left (1-2\,x\right )}^{7/2}}{64}-\frac {832951\,{\left (1-2\,x\right )}^{11/2}}{704}+\frac {121359\,{\left (1-2\,x\right )}^{13/2}}{208}-\frac {53037\,{\left (1-2\,x\right )}^{15/2}}{320}+\frac {13905\,{\left (1-2\,x\right )}^{17/2}}{544}-\frac {2025\,{\left (1-2\,x\right )}^{19/2}}{1216} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 25.53, size = 82, normalized size = 0.89 \[ - \frac {2025 \left (1 - 2 x\right )^{\frac {19}{2}}}{1216} + \frac {13905 \left (1 - 2 x\right )^{\frac {17}{2}}}{544} - \frac {53037 \left (1 - 2 x\right )^{\frac {15}{2}}}{320} + \frac {121359 \left (1 - 2 x\right )^{\frac {13}{2}}}{208} - \frac {832951 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {381073 \left (1 - 2 x\right )^{\frac {9}{2}}}{288} - \frac {41503 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
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