Optimal. Leaf size=66 \[ -\frac {3773}{80} (1-2 x)^{5/2}+\frac {469}{8} (1-2 x)^{7/2}-\frac {119}{4} (1-2 x)^{9/2}+\frac {621}{88} (1-2 x)^{11/2}-\frac {135}{208} (1-2 x)^{13/2} \]
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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 = {78}
\begin {gather*} -\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} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
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 \begin {gather*} -\frac {1}{715} (1-2 x)^{5/2} \left (8494+25310 x+35675 x^2+25515 x^3+7425 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 47, normalized size = 0.71
method | result | size |
gosper | \(-\frac {\left (7425 x^{4}+25515 x^{3}+35675 x^{2}+25310 x +8494\right ) \left (1-2 x \right )^{\frac {5}{2}}}{715}\) | \(30\) |
trager | \(\left (-\frac {540}{13} x^{6}-\frac {14472}{143} x^{5}-\frac {9613}{143} x^{4}+\frac {3189}{143} x^{3}+\frac {31589}{715} x^{2}+\frac {8666}{715} x -\frac {8494}{715}\right ) \sqrt {1-2 x}\) | \(39\) |
risch | \(\frac {\left (29700 x^{6}+72360 x^{5}+48065 x^{4}-15945 x^{3}-31589 x^{2}-8666 x +8494\right ) \left (-1+2 x \right )}{715 \sqrt {1-2 x}}\) | \(45\) |
derivativedivides | \(-\frac {3773 \left (1-2 x \right )^{\frac {5}{2}}}{80}+\frac {469 \left (1-2 x \right )^{\frac {7}{2}}}{8}-\frac {119 \left (1-2 x \right )^{\frac {9}{2}}}{4}+\frac {621 \left (1-2 x \right )^{\frac {11}{2}}}{88}-\frac {135 \left (1-2 x \right )^{\frac {13}{2}}}{208}\) | \(47\) |
default | \(-\frac {3773 \left (1-2 x \right )^{\frac {5}{2}}}{80}+\frac {469 \left (1-2 x \right )^{\frac {7}{2}}}{8}-\frac {119 \left (1-2 x \right )^{\frac {9}{2}}}{4}+\frac {621 \left (1-2 x \right )^{\frac {11}{2}}}{88}-\frac {135 \left (1-2 x \right )^{\frac {13}{2}}}{208}\) | \(47\) |
meijerg | \(-\frac {9 \left (-\frac {8 \sqrt {\pi }}{15}+\frac {4 \sqrt {\pi }\, \left (8 x^{2}-8 x +2\right ) \sqrt {1-2 x}}{15}\right )}{\sqrt {\pi }}+\frac {\frac {148 \sqrt {\pi }}{35}-\frac {37 \sqrt {\pi }\, \left (160 x^{3}-128 x^{2}+8 x +8\right ) \sqrt {1-2 x}}{70}}{\sqrt {\pi }}-\frac {513 \left (-\frac {64 \sqrt {\pi }}{945}+\frac {4 \sqrt {\pi }\, \left (1120 x^{4}-800 x^{3}+24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{945}\right )}{16 \sqrt {\pi }}+\frac {\frac {234 \sqrt {\pi }}{385}-\frac {117 \sqrt {\pi }\, \left (26880 x^{5}-17920 x^{4}+320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{24640}}{\sqrt {\pi }}-\frac {405 \left (-\frac {1024 \sqrt {\pi }}{45045}+\frac {4 \sqrt {\pi }\, \left (147840 x^{6}-94080 x^{5}+1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{45045}\right )}{128 \sqrt {\pi }}\) | \(217\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 46, normalized size = 0.70 \begin {gather*} -\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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.19, size = 39, normalized size = 0.59 \begin {gather*} -\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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 6.67, size = 58, normalized size = 0.88 \begin {gather*} - \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.54, size = 81, normalized size = 1.23 \begin {gather*} -\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} \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 {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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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