Optimal. Leaf size=105 \[ \frac {3195731}{384 (1-2 x)^{3/2}}-\frac {9836211}{128 \sqrt {1-2 x}}-\frac {12973191}{128} \sqrt {1-2 x}+\frac {9504551}{384} (1-2 x)^{3/2}-\frac {4177401}{640} (1-2 x)^{5/2}+\frac {1101465}{896} (1-2 x)^{7/2}-\frac {17925}{128} (1-2 x)^{9/2}+\frac {10125 (1-2 x)^{11/2}}{1408} \]
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Rubi [A]
time = 0.01, antiderivative size = 105, 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 {10125 (1-2 x)^{11/2}}{1408}-\frac {17925}{128} (1-2 x)^{9/2}+\frac {1101465}{896} (1-2 x)^{7/2}-\frac {4177401}{640} (1-2 x)^{5/2}+\frac {9504551}{384} (1-2 x)^{3/2}-\frac {12973191}{128} \sqrt {1-2 x}-\frac {9836211}{128 \sqrt {1-2 x}}+\frac {3195731}{384 (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)^4 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {3195731}{128 (1-2 x)^{5/2}}-\frac {9836211}{128 (1-2 x)^{3/2}}+\frac {12973191}{128 \sqrt {1-2 x}}-\frac {9504551}{128} \sqrt {1-2 x}+\frac {4177401}{128} (1-2 x)^{3/2}-\frac {1101465}{128} (1-2 x)^{5/2}+\frac {161325}{128} (1-2 x)^{7/2}-\frac {10125}{128} (1-2 x)^{9/2}\right ) \, dx\\ &=\frac {3195731}{384 (1-2 x)^{3/2}}-\frac {9836211}{128 \sqrt {1-2 x}}-\frac {12973191}{128} \sqrt {1-2 x}+\frac {9504551}{384} (1-2 x)^{3/2}-\frac {4177401}{640} (1-2 x)^{5/2}+\frac {1101465}{896} (1-2 x)^{7/2}-\frac {17925}{128} (1-2 x)^{9/2}+\frac {10125 (1-2 x)^{11/2}}{1408}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 48, normalized size = 0.46 \begin {gather*} -\frac {173891632-522173856 x+258342648 x^2+77493296 x^3+41201532 x^4+19961775 x^5+6630750 x^6+1063125 x^7}{1155 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 74, normalized size = 0.70
method | result | size |
gosper | \(-\frac {1063125 x^{7}+6630750 x^{6}+19961775 x^{5}+41201532 x^{4}+77493296 x^{3}+258342648 x^{2}-522173856 x +173891632}{1155 \left (1-2 x \right )^{\frac {3}{2}}}\) | \(45\) |
trager | \(-\frac {\left (1063125 x^{7}+6630750 x^{6}+19961775 x^{5}+41201532 x^{4}+77493296 x^{3}+258342648 x^{2}-522173856 x +173891632\right ) \sqrt {1-2 x}}{1155 \left (-1+2 x \right )^{2}}\) | \(52\) |
risch | \(\frac {1063125 x^{7}+6630750 x^{6}+19961775 x^{5}+41201532 x^{4}+77493296 x^{3}+258342648 x^{2}-522173856 x +173891632}{1155 \left (-1+2 x \right ) \sqrt {1-2 x}}\) | \(52\) |
derivativedivides | \(\frac {3195731}{384 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {9504551 \left (1-2 x \right )^{\frac {3}{2}}}{384}-\frac {4177401 \left (1-2 x \right )^{\frac {5}{2}}}{640}+\frac {1101465 \left (1-2 x \right )^{\frac {7}{2}}}{896}-\frac {17925 \left (1-2 x \right )^{\frac {9}{2}}}{128}+\frac {10125 \left (1-2 x \right )^{\frac {11}{2}}}{1408}-\frac {9836211}{128 \sqrt {1-2 x}}-\frac {12973191 \sqrt {1-2 x}}{128}\) | \(74\) |
default | \(\frac {3195731}{384 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {9504551 \left (1-2 x \right )^{\frac {3}{2}}}{384}-\frac {4177401 \left (1-2 x \right )^{\frac {5}{2}}}{640}+\frac {1101465 \left (1-2 x \right )^{\frac {7}{2}}}{896}-\frac {17925 \left (1-2 x \right )^{\frac {9}{2}}}{128}+\frac {10125 \left (1-2 x \right )^{\frac {11}{2}}}{1408}-\frac {9836211}{128 \sqrt {1-2 x}}-\frac {12973191 \sqrt {1-2 x}}{128}\) | \(74\) |
meijerg | \(-\frac {288 \left (\frac {\sqrt {\pi }}{2}-\frac {\sqrt {\pi }}{2 \left (1-2 x \right )^{\frac {3}{2}}}\right )}{\sqrt {\pi }}+\frac {1584 \sqrt {\pi }-\frac {198 \sqrt {\pi }\, \left (-24 x +8\right )}{\left (1-2 x \right )^{\frac {3}{2}}}}{\sqrt {\pi }}-\frac {3732 \left (-4 \sqrt {\pi }+\frac {\sqrt {\pi }\, \left (24 x^{2}-48 x +16\right )}{4 \left (1-2 x \right )^{\frac {3}{2}}}\right )}{\sqrt {\pi }}+\frac {\frac {117184 \sqrt {\pi }}{3}-\frac {1831 \sqrt {\pi }\, \left (64 x^{3}+192 x^{2}-384 x +128\right )}{6 \left (1-2 x \right )^{\frac {3}{2}}}}{\sqrt {\pi }}-\frac {30649 \left (-\frac {64 \sqrt {\pi }}{5}+\frac {\sqrt {\pi }\, \left (96 x^{4}+128 x^{3}+384 x^{2}-768 x +256\right )}{20 \left (1-2 x \right )^{\frac {3}{2}}}\right )}{8 \sqrt {\pi }}+\frac {\frac {230760 \sqrt {\pi }}{7}-\frac {28845 \sqrt {\pi }\, \left (384 x^{5}+384 x^{4}+512 x^{3}+1536 x^{2}-3072 x +1024\right )}{896 \left (1-2 x \right )^{\frac {3}{2}}}}{\sqrt {\pi }}-\frac {15075 \left (-\frac {512 \sqrt {\pi }}{21}+\frac {\sqrt {\pi }\, \left (896 x^{6}+768 x^{5}+768 x^{4}+1024 x^{3}+3072 x^{2}-6144 x +2048\right )}{84 \left (1-2 x \right )^{\frac {3}{2}}}\right )}{32 \sqrt {\pi }}+\frac {\frac {18000 \sqrt {\pi }}{11}-\frac {1125 \sqrt {\pi }\, \left (18432 x^{7}+14336 x^{6}+12288 x^{5}+12288 x^{4}+16384 x^{3}+49152 x^{2}-98304 x +32768\right )}{22528 \left (1-2 x \right )^{\frac {3}{2}}}}{\sqrt {\pi }}\) | \(324\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 69, normalized size = 0.66 \begin {gather*} \frac {10125}{1408} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {17925}{128} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {1101465}{896} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {4177401}{640} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {9504551}{384} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {12973191}{128} \, \sqrt {-2 \, x + 1} + \frac {41503 \, {\left (711 \, x - 317\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 = 0.80, size = 56, normalized size = 0.53 \begin {gather*} -\frac {{\left (1063125 \, x^{7} + 6630750 \, x^{6} + 19961775 \, x^{5} + 41201532 \, x^{4} + 77493296 \, x^{3} + 258342648 \, x^{2} - 522173856 \, x + 173891632\right )} \sqrt {-2 \, x + 1}}{1155 \, {\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 = 21.70, size = 94, normalized size = 0.90 \begin {gather*} \frac {10125 \left (1 - 2 x\right )^{\frac {11}{2}}}{1408} - \frac {17925 \left (1 - 2 x\right )^{\frac {9}{2}}}{128} + \frac {1101465 \left (1 - 2 x\right )^{\frac {7}{2}}}{896} - \frac {4177401 \left (1 - 2 x\right )^{\frac {5}{2}}}{640} + \frac {9504551 \left (1 - 2 x\right )^{\frac {3}{2}}}{384} - \frac {12973191 \sqrt {1 - 2 x}}{128} - \frac {9836211}{128 \sqrt {1 - 2 x}} + \frac {3195731}{384 \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 = 1.09, size = 104, normalized size = 0.99 \begin {gather*} -\frac {10125}{1408} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {17925}{128} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {1101465}{896} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {4177401}{640} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {9504551}{384} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {12973191}{128} \, \sqrt {-2 \, x + 1} - \frac {41503 \, {\left (711 \, x - 317\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 = 68, normalized size = 0.65 \begin {gather*} \frac {\frac {9836211\,x}{64}-\frac {13156451}{192}}{{\left (1-2\,x\right )}^{3/2}}-\frac {12973191\,\sqrt {1-2\,x}}{128}+\frac {9504551\,{\left (1-2\,x\right )}^{3/2}}{384}-\frac {4177401\,{\left (1-2\,x\right )}^{5/2}}{640}+\frac {1101465\,{\left (1-2\,x\right )}^{7/2}}{896}-\frac {17925\,{\left (1-2\,x\right )}^{9/2}}{128}+\frac {10125\,{\left (1-2\,x\right )}^{11/2}}{1408} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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