Optimal. Leaf size=92 \[ -\frac {135}{64} (1-2 x)^{15/2}+\frac {13905}{416} (1-2 x)^{13/2}-\frac {159111}{704} (1-2 x)^{11/2}+\frac {40453}{48} (1-2 x)^{9/2}-\frac {118993}{64} (1-2 x)^{7/2}+\frac {381073}{160} (1-2 x)^{5/2}-\frac {290521}{192} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.02, 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 = {88} \[ -\frac {135}{64} (1-2 x)^{15/2}+\frac {13905}{416} (1-2 x)^{13/2}-\frac {159111}{704} (1-2 x)^{11/2}+\frac {40453}{48} (1-2 x)^{9/2}-\frac {118993}{64} (1-2 x)^{7/2}+\frac {381073}{160} (1-2 x)^{5/2}-\frac {290521}{192} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 88
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 \[ -\frac {(1-2 x)^{3/2} \left (289575 x^6+1425600 x^5+3106755 x^4+3960500 x^3+3298140 x^2+1895832 x+734904\right )}{2145} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 44, normalized size = 0.48 \[ \frac {1}{2145} \, {\left (579150 \, x^{7} + 2561625 \, x^{6} + 4787910 \, x^{5} + 4814245 \, x^{4} + 2635780 \, x^{3} + 493524 \, x^{2} - 426024 \, x - 734904\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 106, normalized size = 1.15 \[ \frac {135}{64} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {13905}{416} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {159111}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {40453}{48} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {118993}{64} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {381073}{160} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {290521}{192} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.43 \[ -\frac {\left (289575 x^{6}+1425600 x^{5}+3106755 x^{4}+3960500 x^{3}+3298140 x^{2}+1895832 x +734904\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{2145} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 64, normalized size = 0.70 \[ -\frac {135}{64} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {13905}{416} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {159111}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {40453}{48} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {118993}{64} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {381073}{160} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {290521}{192} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
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 \[ \frac {381073\,{\left (1-2\,x\right )}^{5/2}}{160}-\frac {290521\,{\left (1-2\,x\right )}^{3/2}}{192}-\frac {118993\,{\left (1-2\,x\right )}^{7/2}}{64}+\frac {40453\,{\left (1-2\,x\right )}^{9/2}}{48}-\frac {159111\,{\left (1-2\,x\right )}^{11/2}}{704}+\frac {13905\,{\left (1-2\,x\right )}^{13/2}}{416}-\frac {135\,{\left (1-2\,x\right )}^{15/2}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.06, size = 82, normalized size = 0.89 \[ - \frac {135 \left (1 - 2 x\right )^{\frac {15}{2}}}{64} + \frac {13905 \left (1 - 2 x\right )^{\frac {13}{2}}}{416} - \frac {159111 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {40453 \left (1 - 2 x\right )^{\frac {9}{2}}}{48} - \frac {118993 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} + \frac {381073 \left (1 - 2 x\right )^{\frac {5}{2}}}{160} - \frac {290521 \left (1 - 2 x\right )^{\frac {3}{2}}}{192} \]
Verification of antiderivative is not currently implemented for this CAS.
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