Optimal. Leaf size=66 \[ -\frac {225}{176} (1-2 x)^{11/2}+\frac {85}{6} (1-2 x)^{9/2}-\frac {3467}{56} (1-2 x)^{7/2}+\frac {1309}{10} (1-2 x)^{5/2}-\frac {5929}{48} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.01, antiderivative size = 66, 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} \begin {gather*} -\frac {225}{176} (1-2 x)^{11/2}+\frac {85}{6} (1-2 x)^{9/2}-\frac {3467}{56} (1-2 x)^{7/2}+\frac {1309}{10} (1-2 x)^{5/2}-\frac {5929}{48} (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (\frac {5929}{16} \sqrt {1-2 x}-\frac {1309}{2} (1-2 x)^{3/2}+\frac {3467}{8} (1-2 x)^{5/2}-\frac {255}{2} (1-2 x)^{7/2}+\frac {225}{16} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {5929}{48} (1-2 x)^{3/2}+\frac {1309}{10} (1-2 x)^{5/2}-\frac {3467}{56} (1-2 x)^{7/2}+\frac {85}{6} (1-2 x)^{9/2}-\frac {225}{176} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} -\frac {(1-2 x)^{3/2} \left (23625 x^4+83650 x^3+125115 x^2+102714 x+48098\right )}{1155} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 60, normalized size = 0.91 \begin {gather*} \frac {-23625 (1-2 x)^{11/2}+261800 (1-2 x)^{9/2}-1144110 (1-2 x)^{7/2}+2419032 (1-2 x)^{5/2}-2282665 (1-2 x)^{3/2}}{18480} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.32, size = 34, normalized size = 0.52 \begin {gather*} \frac {1}{1155} \, {\left (47250 \, x^{5} + 143675 \, x^{4} + 166580 \, x^{3} + 80313 \, x^{2} - 6518 \, x - 48098\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 74, normalized size = 1.12 \begin {gather*} \frac {225}{176} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {85}{6} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {3467}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {1309}{10} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {5929}{48} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 0.45 \begin {gather*} -\frac {\left (23625 x^{4}+83650 x^{3}+125115 x^{2}+102714 x +48098\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{1155} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 46, normalized size = 0.70 \begin {gather*} -\frac {225}{176} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {85}{6} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {3467}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {1309}{10} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {5929}{48} \, {\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 = 0.02, size = 46, normalized size = 0.70 \begin {gather*} \frac {1309\,{\left (1-2\,x\right )}^{5/2}}{10}-\frac {5929\,{\left (1-2\,x\right )}^{3/2}}{48}-\frac {3467\,{\left (1-2\,x\right )}^{7/2}}{56}+\frac {85\,{\left (1-2\,x\right )}^{9/2}}{6}-\frac {225\,{\left (1-2\,x\right )}^{11/2}}{176} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.59, size = 58, normalized size = 0.88 \begin {gather*} - \frac {225 \left (1 - 2 x\right )^{\frac {11}{2}}}{176} + \frac {85 \left (1 - 2 x\right )^{\frac {9}{2}}}{6} - \frac {3467 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} + \frac {1309 \left (1 - 2 x\right )^{\frac {5}{2}}}{10} - \frac {5929 \left (1 - 2 x\right )^{\frac {3}{2}}}{48} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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