Optimal. Leaf size=92 \[ -\frac {290521}{192} (1-2 x)^{3/2}+\frac {381073}{160} (1-2 x)^{5/2}-\frac {118993}{64} (1-2 x)^{7/2}+\frac {40453}{48} (1-2 x)^{9/2}-\frac {159111}{704} (1-2 x)^{11/2}+\frac {13905}{416} (1-2 x)^{13/2}-\frac {135}{64} (1-2 x)^{15/2} \]
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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 {135}{64} (1-2 x)^{15/2}+\frac {13905}{416} (1-2 x)^{13/2}-\frac {159111}{704} (1-2 x)^{11/2}+\frac {40453}{48} (1-2 x)^{9/2}-\frac {118993}{64} (1-2 x)^{7/2}+\frac {381073}{160} (1-2 x)^{5/2}-\frac {290521}{192} (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac {290521}{64} \sqrt {1-2 x}-\frac {381073}{32} (1-2 x)^{3/2}+\frac {832951}{64} (1-2 x)^{5/2}-\frac {121359}{16} (1-2 x)^{7/2}+\frac {159111}{64} (1-2 x)^{9/2}-\frac {13905}{32} (1-2 x)^{11/2}+\frac {2025}{64} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac {290521}{192} (1-2 x)^{3/2}+\frac {381073}{160} (1-2 x)^{5/2}-\frac {118993}{64} (1-2 x)^{7/2}+\frac {40453}{48} (1-2 x)^{9/2}-\frac {159111}{704} (1-2 x)^{11/2}+\frac {13905}{416} (1-2 x)^{13/2}-\frac {135}{64} (1-2 x)^{15/2}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 43, normalized size = 0.47 \begin {gather*} -\frac {(1-2 x)^{3/2} \left (734904+1895832 x+3298140 x^2+3960500 x^3+3106755 x^4+1425600 x^5+289575 x^6\right )}{2145} \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 | \(-\frac {\left (289575 x^{6}+1425600 x^{5}+3106755 x^{4}+3960500 x^{3}+3298140 x^{2}+1895832 x +734904\right ) \left (1-2 x \right )^{\frac {3}{2}}}{2145}\) | \(40\) |
trager | \(\left (270 x^{7}+\frac {15525}{13} x^{6}+\frac {319194}{143} x^{5}+\frac {962849}{429} x^{4}+\frac {527156}{429} x^{3}+\frac {164508}{715} x^{2}-\frac {142008}{715} x -\frac {244968}{715}\right ) \sqrt {1-2 x}\) | \(44\) |
risch | \(-\frac {\left (579150 x^{7}+2561625 x^{6}+4787910 x^{5}+4814245 x^{4}+2635780 x^{3}+493524 x^{2}-426024 x -734904\right ) \left (-1+2 x \right )}{2145 \sqrt {1-2 x}}\) | \(50\) |
derivativedivides | \(-\frac {290521 \left (1-2 x \right )^{\frac {3}{2}}}{192}+\frac {381073 \left (1-2 x \right )^{\frac {5}{2}}}{160}-\frac {118993 \left (1-2 x \right )^{\frac {7}{2}}}{64}+\frac {40453 \left (1-2 x \right )^{\frac {9}{2}}}{48}-\frac {159111 \left (1-2 x \right )^{\frac {11}{2}}}{704}+\frac {13905 \left (1-2 x \right )^{\frac {13}{2}}}{416}-\frac {135 \left (1-2 x \right )^{\frac {15}{2}}}{64}\) | \(65\) |
default | \(-\frac {290521 \left (1-2 x \right )^{\frac {3}{2}}}{192}+\frac {381073 \left (1-2 x \right )^{\frac {5}{2}}}{160}-\frac {118993 \left (1-2 x \right )^{\frac {7}{2}}}{64}+\frac {40453 \left (1-2 x \right )^{\frac {9}{2}}}{48}-\frac {159111 \left (1-2 x \right )^{\frac {11}{2}}}{704}+\frac {13905 \left (1-2 x \right )^{\frac {13}{2}}}{416}-\frac {135 \left (1-2 x \right )^{\frac {15}{2}}}{64}\) | \(65\) |
meijerg | \(\frac {48 \sqrt {\pi }-24 \sqrt {\pi }\, \left (2-4 x \right ) \sqrt {1-2 x}}{\sqrt {\pi }}-\frac {168 \left (-\frac {8 \sqrt {\pi }}{15}+\frac {4 \sqrt {\pi }\, \left (1-2 x \right )^{\frac {3}{2}} \left (6 x +2\right )}{15}\right )}{\sqrt {\pi }}+\frac {\frac {10448 \sqrt {\pi }}{105}-\frac {1306 \sqrt {\pi }\, \left (1-2 x \right )^{\frac {3}{2}} \left (60 x^{2}+24 x +8\right )}{105}}{\sqrt {\pi }}-\frac {1353 \left (-\frac {64 \sqrt {\pi }}{315}+\frac {4 \sqrt {\pi }\, \left (1-2 x \right )^{\frac {3}{2}} \left (280 x^{3}+120 x^{2}+48 x +16\right )}{315}\right )}{4 \sqrt {\pi }}+\frac {\frac {11208 \sqrt {\pi }}{385}-\frac {1401 \sqrt {\pi }\, \left (1-2 x \right )^{\frac {3}{2}} \left (5040 x^{4}+2240 x^{3}+960 x^{2}+384 x +128\right )}{6160}}{\sqrt {\pi }}-\frac {3915 \left (-\frac {1024 \sqrt {\pi }}{9009}+\frac {4 \sqrt {\pi }\, \left (1-2 x \right )^{\frac {3}{2}} \left (22176 x^{5}+10080 x^{4}+4480 x^{3}+1920 x^{2}+768 x +256\right )}{9009}\right )}{64 \sqrt {\pi }}+\frac {\frac {720 \sqrt {\pi }}{1001}-\frac {45 \sqrt {\pi }\, \left (1-2 x \right )^{\frac {3}{2}} \left (192192 x^{6}+88704 x^{5}+40320 x^{4}+17920 x^{3}+7680 x^{2}+3072 x +1024\right )}{64064}}{\sqrt {\pi }}\) | \(273\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 64, normalized size = 0.70 \begin {gather*} -\frac {135}{64} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {13905}{416} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {159111}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {40453}{48} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {118993}{64} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {381073}{160} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {290521}{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 = 0.59, size = 44, normalized size = 0.48 \begin {gather*} \frac {1}{2145} \, {\left (579150 \, x^{7} + 2561625 \, x^{6} + 4787910 \, x^{5} + 4814245 \, x^{4} + 2635780 \, x^{3} + 493524 \, x^{2} - 426024 \, x - 734904\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.49, size = 82, normalized size = 0.89 \begin {gather*} - \frac {135 \left (1 - 2 x\right )^{\frac {15}{2}}}{64} + \frac {13905 \left (1 - 2 x\right )^{\frac {13}{2}}}{416} - \frac {159111 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {40453 \left (1 - 2 x\right )^{\frac {9}{2}}}{48} - \frac {118993 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} + \frac {381073 \left (1 - 2 x\right )^{\frac {5}{2}}}{160} - \frac {290521 \left (1 - 2 x\right )^{\frac {3}{2}}}{192} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.85, size = 106, normalized size = 1.15 \begin {gather*} \frac {135}{64} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {13905}{416} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {159111}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {40453}{48} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {118993}{64} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {381073}{160} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {290521}{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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Mupad [B]
time = 1.18, size = 64, normalized size = 0.70 \begin {gather*} \frac {381073\,{\left (1-2\,x\right )}^{5/2}}{160}-\frac {290521\,{\left (1-2\,x\right )}^{3/2}}{192}-\frac {118993\,{\left (1-2\,x\right )}^{7/2}}{64}+\frac {40453\,{\left (1-2\,x\right )}^{9/2}}{48}-\frac {159111\,{\left (1-2\,x\right )}^{11/2}}{704}+\frac {13905\,{\left (1-2\,x\right )}^{13/2}}{416}-\frac {135\,{\left (1-2\,x\right )}^{15/2}}{64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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