Optimal. Leaf size=27 \[ -\frac {11}{10} (1-2 x)^{5/2}+\frac {5}{14} (1-2 x)^{7/2} \]
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Rubi [A]
time = 0.00, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45}
\begin {gather*} \frac {5}{14} (1-2 x)^{7/2}-\frac {11}{10} (1-2 x)^{5/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (1-2 x)^{3/2} (3+5 x) \, dx &=\int \left (\frac {11}{2} (1-2 x)^{3/2}-\frac {5}{2} (1-2 x)^{5/2}\right ) \, dx\\ &=-\frac {11}{10} (1-2 x)^{5/2}+\frac {5}{14} (1-2 x)^{7/2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 18, normalized size = 0.67 \begin {gather*} -\frac {1}{35} (1-2 x)^{5/2} (26+25 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 20, normalized size = 0.74
method | result | size |
gosper | \(-\frac {\left (25 x +26\right ) \left (1-2 x \right )^{\frac {5}{2}}}{35}\) | \(15\) |
derivativedivides | \(-\frac {11 \left (1-2 x \right )^{\frac {5}{2}}}{10}+\frac {5 \left (1-2 x \right )^{\frac {7}{2}}}{14}\) | \(20\) |
default | \(-\frac {11 \left (1-2 x \right )^{\frac {5}{2}}}{10}+\frac {5 \left (1-2 x \right )^{\frac {7}{2}}}{14}\) | \(20\) |
trager | \(\left (-\frac {20}{7} x^{3}-\frac {4}{35} x^{2}+\frac {79}{35} x -\frac {26}{35}\right ) \sqrt {1-2 x}\) | \(24\) |
risch | \(\frac {\left (100 x^{3}+4 x^{2}-79 x +26\right ) \left (-1+2 x \right )}{35 \sqrt {1-2 x}}\) | \(30\) |
meijerg | \(-\frac {9 \left (-\frac {8 \sqrt {\pi }}{15}+\frac {4 \sqrt {\pi }\, \left (8 x^{2}-8 x +2\right ) \sqrt {1-2 x}}{15}\right )}{8 \sqrt {\pi }}+\frac {\frac {\sqrt {\pi }}{7}-\frac {\sqrt {\pi }\, \left (160 x^{3}-128 x^{2}+8 x +8\right ) \sqrt {1-2 x}}{56}}{\sqrt {\pi }}\) | \(73\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 19, normalized size = 0.70 \begin {gather*} \frac {5}{14} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {11}{10} \, {\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 = 1.17, size = 24, normalized size = 0.89 \begin {gather*} -\frac {1}{35} \, {\left (100 \, x^{3} + 4 \, x^{2} - 79 \, x + 26\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 54 vs.
\(2 (22) = 44\).
time = 0.10, size = 54, normalized size = 2.00 \begin {gather*} - \frac {20 x^{3} \sqrt {1 - 2 x}}{7} - \frac {4 x^{2} \sqrt {1 - 2 x}}{35} + \frac {79 x \sqrt {1 - 2 x}}{35} - \frac {26 \sqrt {1 - 2 x}}{35} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.06, size = 33, normalized size = 1.22 \begin {gather*} -\frac {5}{14} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {11}{10} \, {\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 = 14, normalized size = 0.52 \begin {gather*} -\frac {{\left (1-2\,x\right )}^{5/2}\,\left (50\,x+52\right )}{70} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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