Optimal. Leaf size=79 \[ -\frac {3773}{32} (1-2 x)^{7/2}+\frac {57281}{288} (1-2 x)^{9/2}-\frac {24843}{176} (1-2 x)^{11/2}+\frac {10773}{208} (1-2 x)^{13/2}-\frac {1557}{160} (1-2 x)^{15/2}+\frac {405}{544} (1-2 x)^{17/2} \]
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Rubi [A]
time = 0.01, antiderivative size = 79, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {78}
\begin {gather*} \frac {405}{544} (1-2 x)^{17/2}-\frac {1557}{160} (1-2 x)^{15/2}+\frac {10773}{208} (1-2 x)^{13/2}-\frac {24843}{176} (1-2 x)^{11/2}+\frac {57281}{288} (1-2 x)^{9/2}-\frac {3773}{32} (1-2 x)^{7/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x)^4 (3+5 x) \, dx &=\int \left (\frac {26411}{32} (1-2 x)^{5/2}-\frac {57281}{32} (1-2 x)^{7/2}+\frac {24843}{16} (1-2 x)^{9/2}-\frac {10773}{16} (1-2 x)^{11/2}+\frac {4671}{32} (1-2 x)^{13/2}-\frac {405}{32} (1-2 x)^{15/2}\right ) \, dx\\ &=-\frac {3773}{32} (1-2 x)^{7/2}+\frac {57281}{288} (1-2 x)^{9/2}-\frac {24843}{176} (1-2 x)^{11/2}+\frac {10773}{208} (1-2 x)^{13/2}-\frac {1557}{160} (1-2 x)^{15/2}+\frac {405}{544} (1-2 x)^{17/2}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 38, normalized size = 0.48 \begin {gather*} -\frac {(1-2 x)^{7/2} \left (1899184+8043328 x+16066296 x^2+17777232 x^3+10517364 x^4+2606175 x^5\right )}{109395} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 56, normalized size = 0.71
method | result | size |
gosper | \(-\frac {\left (2606175 x^{5}+10517364 x^{4}+17777232 x^{3}+16066296 x^{2}+8043328 x +1899184\right ) \left (1-2 x \right )^{\frac {7}{2}}}{109395}\) | \(35\) |
trager | \(\left (\frac {3240}{17} x^{8}+\frac {41076}{85} x^{7}+\frac {319662}{1105} x^{6}-\frac {2699823}{12155} x^{5}-\frac {6460580}{21879} x^{4}-\frac {541184}{21879} x^{3}+\frac {3134488}{36465} x^{2}+\frac {3351776}{109395} x -\frac {1899184}{109395}\right ) \sqrt {1-2 x}\) | \(49\) |
risch | \(-\frac {\left (20849400 x^{8}+52864812 x^{7}+31646538 x^{6}-24298407 x^{5}-32302900 x^{4}-2705920 x^{3}+9403464 x^{2}+3351776 x -1899184\right ) \left (-1+2 x \right )}{109395 \sqrt {1-2 x}}\) | \(55\) |
derivativedivides | \(-\frac {3773 \left (1-2 x \right )^{\frac {7}{2}}}{32}+\frac {57281 \left (1-2 x \right )^{\frac {9}{2}}}{288}-\frac {24843 \left (1-2 x \right )^{\frac {11}{2}}}{176}+\frac {10773 \left (1-2 x \right )^{\frac {13}{2}}}{208}-\frac {1557 \left (1-2 x \right )^{\frac {15}{2}}}{160}+\frac {405 \left (1-2 x \right )^{\frac {17}{2}}}{544}\) | \(56\) |
default | \(-\frac {3773 \left (1-2 x \right )^{\frac {7}{2}}}{32}+\frac {57281 \left (1-2 x \right )^{\frac {9}{2}}}{288}-\frac {24843 \left (1-2 x \right )^{\frac {11}{2}}}{176}+\frac {10773 \left (1-2 x \right )^{\frac {13}{2}}}{208}-\frac {1557 \left (1-2 x \right )^{\frac {15}{2}}}{160}+\frac {405 \left (1-2 x \right )^{\frac {17}{2}}}{544}\) | \(56\) |
meijerg | \(\frac {\frac {48 \sqrt {\pi }}{7}-\frac {24 \sqrt {\pi }\, \left (-16 x^{3}+24 x^{2}-12 x +2\right ) \sqrt {1-2 x}}{7}}{\sqrt {\pi }}-\frac {345 \left (-\frac {32 \sqrt {\pi }}{945}+\frac {4 \sqrt {\pi }\, \left (-448 x^{4}+608 x^{3}-240 x^{2}+8 x +8\right ) \sqrt {1-2 x}}{945}\right )}{2 \sqrt {\pi }}+\frac {\frac {752 \sqrt {\pi }}{231}-\frac {47 \sqrt {\pi }\, \left (-4032 x^{5}+5152 x^{4}-1808 x^{3}+24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{231}}{\sqrt {\pi }}-\frac {405 \left (-\frac {256 \sqrt {\pi }}{45045}+\frac {2 \sqrt {\pi }\, \left (-118272 x^{6}+145152 x^{5}-47488 x^{4}+320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{45045}\right )}{2 \sqrt {\pi }}+\frac {\frac {168 \sqrt {\pi }}{715}-\frac {21 \sqrt {\pi }\, \left (-768768 x^{7}+916608 x^{6}-286272 x^{5}+1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{22880}}{\sqrt {\pi }}-\frac {6075 \left (-\frac {4096 \sqrt {\pi }}{2297295}+\frac {4 \sqrt {\pi }\, \left (-9225216 x^{8}+10762752 x^{7}-3252480 x^{6}+8064 x^{5}+4480 x^{4}+2560 x^{3}+1536 x^{2}+1024 x +1024\right ) \sqrt {1-2 x}}{2297295}\right )}{512 \sqrt {\pi }}\) | \(305\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 55, normalized size = 0.70 \begin {gather*} \frac {405}{544} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} - \frac {1557}{160} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {10773}{208} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {24843}{176} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {57281}{288} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {3773}{32} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.03, size = 49, normalized size = 0.62 \begin {gather*} \frac {1}{109395} \, {\left (20849400 \, x^{8} + 52864812 \, x^{7} + 31646538 \, x^{6} - 24298407 \, x^{5} - 32302900 \, x^{4} - 2705920 \, x^{3} + 9403464 \, x^{2} + 3351776 \, x - 1899184\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 13.59, size = 70, normalized size = 0.89 \begin {gather*} \frac {405 \left (1 - 2 x\right )^{\frac {17}{2}}}{544} - \frac {1557 \left (1 - 2 x\right )^{\frac {15}{2}}}{160} + \frac {10773 \left (1 - 2 x\right )^{\frac {13}{2}}}{208} - \frac {24843 \left (1 - 2 x\right )^{\frac {11}{2}}}{176} + \frac {57281 \left (1 - 2 x\right )^{\frac {9}{2}}}{288} - \frac {3773 \left (1 - 2 x\right )^{\frac {7}{2}}}{32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.53, size = 97, normalized size = 1.23 \begin {gather*} \frac {405}{544} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} + \frac {1557}{160} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {10773}{208} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {24843}{176} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {57281}{288} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {3773}{32} \, {\left (2 \, x - 1\right )}^{3} \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 = 55, normalized size = 0.70 \begin {gather*} \frac {57281\,{\left (1-2\,x\right )}^{9/2}}{288}-\frac {3773\,{\left (1-2\,x\right )}^{7/2}}{32}-\frac {24843\,{\left (1-2\,x\right )}^{11/2}}{176}+\frac {10773\,{\left (1-2\,x\right )}^{13/2}}{208}-\frac {1557\,{\left (1-2\,x\right )}^{15/2}}{160}+\frac {405\,{\left (1-2\,x\right )}^{17/2}}{544} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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