Optimal. Leaf size=92 \[ \frac {456533}{192 (1-2 x)^{3/2}}-\frac {302379}{16 \sqrt {1-2 x}}-\frac {1334949}{64} \sqrt {1-2 x}+\frac {98209}{24} (1-2 x)^{3/2}-\frac {52011}{64} (1-2 x)^{5/2}+\frac {11475}{112} (1-2 x)^{7/2}-\frac {375}{64} (1-2 x)^{9/2} \]
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Rubi [A]
time = 0.01, 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 = {90}
\begin {gather*} -\frac {375}{64} (1-2 x)^{9/2}+\frac {11475}{112} (1-2 x)^{7/2}-\frac {52011}{64} (1-2 x)^{5/2}+\frac {98209}{24} (1-2 x)^{3/2}-\frac {1334949}{64} \sqrt {1-2 x}-\frac {302379}{16 \sqrt {1-2 x}}+\frac {456533}{192 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {456533}{64 (1-2 x)^{5/2}}-\frac {302379}{16 (1-2 x)^{3/2}}+\frac {1334949}{64 \sqrt {1-2 x}}-\frac {98209}{8} \sqrt {1-2 x}+\frac {260055}{64} (1-2 x)^{3/2}-\frac {11475}{16} (1-2 x)^{5/2}+\frac {3375}{64} (1-2 x)^{7/2}\right ) \, dx\\ &=\frac {456533}{192 (1-2 x)^{3/2}}-\frac {302379}{16 \sqrt {1-2 x}}-\frac {1334949}{64} \sqrt {1-2 x}+\frac {98209}{24} (1-2 x)^{3/2}-\frac {52011}{64} (1-2 x)^{5/2}+\frac {11475}{112} (1-2 x)^{7/2}-\frac {375}{64} (1-2 x)^{9/2}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 43, normalized size = 0.47 \begin {gather*} -\frac {714074-2146758 x+1051833 x^2+293785 x^3+130464 x^4+45225 x^5+7875 x^6}{21 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 65, normalized size = 0.71
method | result | size |
gosper | \(-\frac {7875 x^{6}+45225 x^{5}+130464 x^{4}+293785 x^{3}+1051833 x^{2}-2146758 x +714074}{21 \left (1-2 x \right )^{\frac {3}{2}}}\) | \(40\) |
trager | \(-\frac {\left (7875 x^{6}+45225 x^{5}+130464 x^{4}+293785 x^{3}+1051833 x^{2}-2146758 x +714074\right ) \sqrt {1-2 x}}{21 \left (-1+2 x \right )^{2}}\) | \(47\) |
risch | \(\frac {7875 x^{6}+45225 x^{5}+130464 x^{4}+293785 x^{3}+1051833 x^{2}-2146758 x +714074}{21 \left (-1+2 x \right ) \sqrt {1-2 x}}\) | \(47\) |
derivativedivides | \(\frac {456533}{192 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {98209 \left (1-2 x \right )^{\frac {3}{2}}}{24}-\frac {52011 \left (1-2 x \right )^{\frac {5}{2}}}{64}+\frac {11475 \left (1-2 x \right )^{\frac {7}{2}}}{112}-\frac {375 \left (1-2 x \right )^{\frac {9}{2}}}{64}-\frac {302379}{16 \sqrt {1-2 x}}-\frac {1334949 \sqrt {1-2 x}}{64}\) | \(65\) |
default | \(\frac {456533}{192 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {98209 \left (1-2 x \right )^{\frac {3}{2}}}{24}-\frac {52011 \left (1-2 x \right )^{\frac {5}{2}}}{64}+\frac {11475 \left (1-2 x \right )^{\frac {7}{2}}}{112}-\frac {375 \left (1-2 x \right )^{\frac {9}{2}}}{64}-\frac {302379}{16 \sqrt {1-2 x}}-\frac {1334949 \sqrt {1-2 x}}{64}\) | \(65\) |
meijerg | \(-\frac {144 \left (\frac {\sqrt {\pi }}{2}-\frac {\sqrt {\pi }}{2 \left (1-2 x \right )^{\frac {3}{2}}}\right )}{\sqrt {\pi }}+\frac {684 \sqrt {\pi }-\frac {171 \sqrt {\pi }\, \left (-24 x +8\right )}{2 \left (1-2 x \right )^{\frac {3}{2}}}}{\sqrt {\pi }}-\frac {1353 \left (-4 \sqrt {\pi }+\frac {\sqrt {\pi }\, \left (24 x^{2}-48 x +16\right )}{4 \left (1-2 x \right )^{\frac {3}{2}}}\right )}{\sqrt {\pi }}+\frac {\frac {34238 \sqrt {\pi }}{3}-\frac {17119 \sqrt {\pi }\, \left (64 x^{3}+192 x^{2}-384 x +128\right )}{192 \left (1-2 x \right )^{\frac {3}{2}}}}{\sqrt {\pi }}-\frac {6765 \left (-\frac {64 \sqrt {\pi }}{5}+\frac {\sqrt {\pi }\, \left (96 x^{4}+128 x^{3}+384 x^{2}-768 x +256\right )}{20 \left (1-2 x \right )^{\frac {3}{2}}}\right )}{8 \sqrt {\pi }}+\frac {\frac {34200 \sqrt {\pi }}{7}-\frac {4275 \sqrt {\pi }\, \left (384 x^{5}+384 x^{4}+512 x^{3}+1536 x^{2}-3072 x +1024\right )}{896 \left (1-2 x \right )^{\frac {3}{2}}}}{\sqrt {\pi }}-\frac {1125 \left (-\frac {512 \sqrt {\pi }}{21}+\frac {\sqrt {\pi }\, \left (896 x^{6}+768 x^{5}+768 x^{4}+1024 x^{3}+3072 x^{2}-6144 x +2048\right )}{84 \left (1-2 x \right )^{\frac {3}{2}}}\right )}{32 \sqrt {\pi }}\) | \(266\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 60, normalized size = 0.65 \begin {gather*} -\frac {375}{64} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {11475}{112} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {52011}{64} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {98209}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {1334949}{64} \, \sqrt {-2 \, x + 1} + \frac {5929 \, {\left (1224 \, x - 535\right )}}{192 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.98, size = 51, normalized size = 0.55 \begin {gather*} -\frac {{\left (7875 \, x^{6} + 45225 \, x^{5} + 130464 \, x^{4} + 293785 \, x^{3} + 1051833 \, x^{2} - 2146758 \, x + 714074\right )} \sqrt {-2 \, x + 1}}{21 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 17.03, size = 82, normalized size = 0.89 \begin {gather*} - \frac {375 \left (1 - 2 x\right )^{\frac {9}{2}}}{64} + \frac {11475 \left (1 - 2 x\right )^{\frac {7}{2}}}{112} - \frac {52011 \left (1 - 2 x\right )^{\frac {5}{2}}}{64} + \frac {98209 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} - \frac {1334949 \sqrt {1 - 2 x}}{64} - \frac {302379}{16 \sqrt {1 - 2 x}} + \frac {456533}{192 \left (1 - 2 x\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.75, size = 88, normalized size = 0.96 \begin {gather*} -\frac {375}{64} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {11475}{112} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {52011}{64} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {98209}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {1334949}{64} \, \sqrt {-2 \, x + 1} - \frac {5929 \, {\left (1224 \, x - 535\right )}}{192 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 59, normalized size = 0.64 \begin {gather*} \frac {\frac {302379\,x}{8}-\frac {3172015}{192}}{{\left (1-2\,x\right )}^{3/2}}-\frac {1334949\,\sqrt {1-2\,x}}{64}+\frac {98209\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {52011\,{\left (1-2\,x\right )}^{5/2}}{64}+\frac {11475\,{\left (1-2\,x\right )}^{7/2}}{112}-\frac {375\,{\left (1-2\,x\right )}^{9/2}}{64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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