Optimal. Leaf size=66 \[ -\frac {135}{208} (1-2 x)^{13/2}+\frac {621}{88} (1-2 x)^{11/2}-\frac {119}{4} (1-2 x)^{9/2}+\frac {469}{8} (1-2 x)^{7/2}-\frac {3773}{80} (1-2 x)^{5/2} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ -\frac {135}{208} (1-2 x)^{13/2}+\frac {621}{88} (1-2 x)^{11/2}-\frac {119}{4} (1-2 x)^{9/2}+\frac {469}{8} (1-2 x)^{7/2}-\frac {3773}{80} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x) \, dx &=\int \left (\frac {3773}{16} (1-2 x)^{3/2}-\frac {3283}{8} (1-2 x)^{5/2}+\frac {1071}{4} (1-2 x)^{7/2}-\frac {621}{8} (1-2 x)^{9/2}+\frac {135}{16} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac {3773}{80} (1-2 x)^{5/2}+\frac {469}{8} (1-2 x)^{7/2}-\frac {119}{4} (1-2 x)^{9/2}+\frac {621}{88} (1-2 x)^{11/2}-\frac {135}{208} (1-2 x)^{13/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \[ -\frac {1}{715} (1-2 x)^{5/2} \left (7425 x^4+25515 x^3+35675 x^2+25310 x+8494\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 39, normalized size = 0.59 \[ -\frac {1}{715} \, {\left (29700 \, x^{6} + 72360 \, x^{5} + 48065 \, x^{4} - 15945 \, x^{3} - 31589 \, x^{2} - 8666 \, x + 8494\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.60, size = 81, normalized size = 1.23 \[ -\frac {135}{208} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {621}{88} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {119}{4} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {469}{8} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {3773}{80} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} \]
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 \[ -\frac {\left (7425 x^{4}+25515 x^{3}+35675 x^{2}+25310 x +8494\right ) \left (-2 x +1\right )^{\frac {5}{2}}}{715} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 46, normalized size = 0.70 \[ -\frac {135}{208} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {621}{88} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {119}{4} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {469}{8} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {3773}{80} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} \]
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 \[ \frac {469\,{\left (1-2\,x\right )}^{7/2}}{8}-\frac {3773\,{\left (1-2\,x\right )}^{5/2}}{80}-\frac {119\,{\left (1-2\,x\right )}^{9/2}}{4}+\frac {621\,{\left (1-2\,x\right )}^{11/2}}{88}-\frac {135\,{\left (1-2\,x\right )}^{13/2}}{208} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 13.53, size = 58, normalized size = 0.88 \[ - \frac {135 \left (1 - 2 x\right )^{\frac {13}{2}}}{208} + \frac {621 \left (1 - 2 x\right )^{\frac {11}{2}}}{88} - \frac {119 \left (1 - 2 x\right )^{\frac {9}{2}}}{4} + \frac {469 \left (1 - 2 x\right )^{\frac {7}{2}}}{8} - \frac {3773 \left (1 - 2 x\right )^{\frac {5}{2}}}{80} \]
Verification of antiderivative is not currently implemented for this CAS.
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