Optimal. Leaf size=79 \[ -\frac {26411}{32} \sqrt {1-2 x}+\frac {57281}{96} (1-2 x)^{3/2}-\frac {24843}{80} (1-2 x)^{5/2}+\frac {1539}{16} (1-2 x)^{7/2}-\frac {519}{32} (1-2 x)^{9/2}+\frac {405}{352} (1-2 x)^{11/2} \]
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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}{352} (1-2 x)^{11/2}-\frac {519}{32} (1-2 x)^{9/2}+\frac {1539}{16} (1-2 x)^{7/2}-\frac {24843}{80} (1-2 x)^{5/2}+\frac {57281}{96} (1-2 x)^{3/2}-\frac {26411}{32} \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4 (3+5 x)}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {26411}{32 \sqrt {1-2 x}}-\frac {57281}{32} \sqrt {1-2 x}+\frac {24843}{16} (1-2 x)^{3/2}-\frac {10773}{16} (1-2 x)^{5/2}+\frac {4671}{32} (1-2 x)^{7/2}-\frac {405}{32} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {26411}{32} \sqrt {1-2 x}+\frac {57281}{96} (1-2 x)^{3/2}-\frac {24843}{80} (1-2 x)^{5/2}+\frac {1539}{16} (1-2 x)^{7/2}-\frac {519}{32} (1-2 x)^{9/2}+\frac {405}{352} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 38, normalized size = 0.48 \begin {gather*} -\frac {1}{165} \sqrt {1-2 x} \left (75584+67664 x+71136 x^2+56520 x^3+27630 x^4+6075 x^5\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 56, normalized size = 0.71
method | result | size |
trager | \(\left (-\frac {405}{11} x^{5}-\frac {1842}{11} x^{4}-\frac {3768}{11} x^{3}-\frac {23712}{55} x^{2}-\frac {67664}{165} x -\frac {75584}{165}\right ) \sqrt {1-2 x}\) | \(34\) |
gosper | \(-\frac {\left (6075 x^{5}+27630 x^{4}+56520 x^{3}+71136 x^{2}+67664 x +75584\right ) \sqrt {1-2 x}}{165}\) | \(35\) |
risch | \(\frac {\left (-1+2 x \right ) \left (6075 x^{5}+27630 x^{4}+56520 x^{3}+71136 x^{2}+67664 x +75584\right )}{165 \sqrt {1-2 x}}\) | \(40\) |
derivativedivides | \(\frac {57281 \left (1-2 x \right )^{\frac {3}{2}}}{96}-\frac {24843 \left (1-2 x \right )^{\frac {5}{2}}}{80}+\frac {1539 \left (1-2 x \right )^{\frac {7}{2}}}{16}-\frac {519 \left (1-2 x \right )^{\frac {9}{2}}}{32}+\frac {405 \left (1-2 x \right )^{\frac {11}{2}}}{352}-\frac {26411 \sqrt {1-2 x}}{32}\) | \(56\) |
default | \(\frac {57281 \left (1-2 x \right )^{\frac {3}{2}}}{96}-\frac {24843 \left (1-2 x \right )^{\frac {5}{2}}}{80}+\frac {1539 \left (1-2 x \right )^{\frac {7}{2}}}{16}-\frac {519 \left (1-2 x \right )^{\frac {9}{2}}}{32}+\frac {405 \left (1-2 x \right )^{\frac {11}{2}}}{352}-\frac {26411 \sqrt {1-2 x}}{32}\) | \(56\) |
meijerg | \(-\frac {24 \left (-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {1-2 x}\right )}{\sqrt {\pi }}+\frac {\frac {368 \sqrt {\pi }}{3}-\frac {46 \sqrt {\pi }\, \left (8 x +8\right ) \sqrt {1-2 x}}{3}}{\sqrt {\pi }}-\frac {141 \left (-\frac {16 \sqrt {\pi }}{15}+\frac {\sqrt {\pi }\, \left (24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{15}\right )}{\sqrt {\pi }}+\frac {\frac {3456 \sqrt {\pi }}{35}-\frac {27 \sqrt {\pi }\, \left (320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{35}}{\sqrt {\pi }}-\frac {1323 \left (-\frac {256 \sqrt {\pi }}{315}+\frac {\sqrt {\pi }\, \left (1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{315}\right )}{32 \sqrt {\pi }}+\frac {\frac {360 \sqrt {\pi }}{77}-\frac {45 \sqrt {\pi }\, \left (8064 x^{5}+4480 x^{4}+2560 x^{3}+1536 x^{2}+1024 x +1024\right ) \sqrt {1-2 x}}{9856}}{\sqrt {\pi }}\) | \(215\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 55, normalized size = 0.70 \begin {gather*} \frac {405}{352} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {519}{32} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {1539}{16} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {24843}{80} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {57281}{96} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {26411}{32} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.81, size = 34, normalized size = 0.43 \begin {gather*} -\frac {1}{165} \, {\left (6075 \, x^{5} + 27630 \, x^{4} + 56520 \, x^{3} + 71136 \, x^{2} + 67664 \, x + 75584\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 32.74, size = 70, normalized size = 0.89 \begin {gather*} \frac {405 \left (1 - 2 x\right )^{\frac {11}{2}}}{352} - \frac {519 \left (1 - 2 x\right )^{\frac {9}{2}}}{32} + \frac {1539 \left (1 - 2 x\right )^{\frac {7}{2}}}{16} - \frac {24843 \left (1 - 2 x\right )^{\frac {5}{2}}}{80} + \frac {57281 \left (1 - 2 x\right )^{\frac {3}{2}}}{96} - \frac {26411 \sqrt {1 - 2 x}}{32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.53, size = 83, normalized size = 1.05 \begin {gather*} -\frac {405}{352} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {519}{32} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {1539}{16} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {24843}{80} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {57281}{96} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {26411}{32} \, \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 )}^{3/2}}{96}-\frac {26411\,\sqrt {1-2\,x}}{32}-\frac {24843\,{\left (1-2\,x\right )}^{5/2}}{80}+\frac {1539\,{\left (1-2\,x\right )}^{7/2}}{16}-\frac {519\,{\left (1-2\,x\right )}^{9/2}}{32}+\frac {405\,{\left (1-2\,x\right )}^{11/2}}{352} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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