Optimal. Leaf size=92 \[ -\frac {225}{64} (1-2 x)^{15/2}+\frac {11475}{208} (1-2 x)^{13/2}-\frac {260055}{704} (1-2 x)^{11/2}+\frac {98209}{72} (1-2 x)^{9/2}-\frac {190707}{64} (1-2 x)^{7/2}+\frac {302379}{80} (1-2 x)^{5/2}-\frac {456533}{192} (1-2 x)^{3/2} \]
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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} \[ -\frac {225}{64} (1-2 x)^{15/2}+\frac {11475}{208} (1-2 x)^{13/2}-\frac {260055}{704} (1-2 x)^{11/2}+\frac {98209}{72} (1-2 x)^{9/2}-\frac {190707}{64} (1-2 x)^{7/2}+\frac {302379}{80} (1-2 x)^{5/2}-\frac {456533}{192} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (\frac {456533}{64} \sqrt {1-2 x}-\frac {302379}{16} (1-2 x)^{3/2}+\frac {1334949}{64} (1-2 x)^{5/2}-\frac {98209}{8} (1-2 x)^{7/2}+\frac {260055}{64} (1-2 x)^{9/2}-\frac {11475}{16} (1-2 x)^{11/2}+\frac {3375}{64} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac {456533}{192} (1-2 x)^{3/2}+\frac {302379}{80} (1-2 x)^{5/2}-\frac {190707}{64} (1-2 x)^{7/2}+\frac {98209}{72} (1-2 x)^{9/2}-\frac {260055}{704} (1-2 x)^{11/2}+\frac {11475}{208} (1-2 x)^{13/2}-\frac {225}{64} (1-2 x)^{15/2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 43, normalized size = 0.47 \[ -\frac {(1-2 x)^{3/2} \left (1447875 x^6+7016625 x^5+15061950 x^4+18934285 x^3+15577455 x^2+8871906 x+3420622\right )}{6435} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.94, size = 44, normalized size = 0.48 \[ \frac {1}{6435} \, {\left (2895750 \, x^{7} + 12585375 \, x^{6} + 23107275 \, x^{5} + 22806620 \, x^{4} + 12220625 \, x^{3} + 2166357 \, x^{2} - 2030662 \, x - 3420622\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.27, size = 106, normalized size = 1.15 \[ \frac {225}{64} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {11475}{208} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {260055}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {98209}{72} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {190707}{64} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {302379}{80} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {456533}{192} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
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 \[ -\frac {\left (1447875 x^{6}+7016625 x^{5}+15061950 x^{4}+18934285 x^{3}+15577455 x^{2}+8871906 x +3420622\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{6435} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 64, normalized size = 0.70 \[ -\frac {225}{64} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {11475}{208} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {260055}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {98209}{72} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {190707}{64} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {302379}{80} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {456533}{192} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 64, normalized size = 0.70 \[ \frac {302379\,{\left (1-2\,x\right )}^{5/2}}{80}-\frac {456533\,{\left (1-2\,x\right )}^{3/2}}{192}-\frac {190707\,{\left (1-2\,x\right )}^{7/2}}{64}+\frac {98209\,{\left (1-2\,x\right )}^{9/2}}{72}-\frac {260055\,{\left (1-2\,x\right )}^{11/2}}{704}+\frac {11475\,{\left (1-2\,x\right )}^{13/2}}{208}-\frac {225\,{\left (1-2\,x\right )}^{15/2}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.06, size = 82, normalized size = 0.89 \[ - \frac {225 \left (1 - 2 x\right )^{\frac {15}{2}}}{64} + \frac {11475 \left (1 - 2 x\right )^{\frac {13}{2}}}{208} - \frac {260055 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {98209 \left (1 - 2 x\right )^{\frac {9}{2}}}{72} - \frac {190707 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} + \frac {302379 \left (1 - 2 x\right )^{\frac {5}{2}}}{80} - \frac {456533 \left (1 - 2 x\right )^{\frac {3}{2}}}{192} \]
Verification of antiderivative is not currently implemented for this CAS.
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