Optimal. Leaf size=79 \[ \frac {405}{224} (1-2 x)^{7/2}-\frac {4671}{160} (1-2 x)^{5/2}+\frac {3591}{16} (1-2 x)^{3/2}-\frac {24843}{16} \sqrt {1-2 x}-\frac {57281}{32 \sqrt {1-2 x}}+\frac {26411}{96 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.01, antiderivative size = 79, 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} \[ \frac {405}{224} (1-2 x)^{7/2}-\frac {4671}{160} (1-2 x)^{5/2}+\frac {3591}{16} (1-2 x)^{3/2}-\frac {24843}{16} \sqrt {1-2 x}-\frac {57281}{32 \sqrt {1-2 x}}+\frac {26411}{96 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4 (3+5 x)}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {26411}{32 (1-2 x)^{5/2}}-\frac {57281}{32 (1-2 x)^{3/2}}+\frac {24843}{16 \sqrt {1-2 x}}-\frac {10773}{16} \sqrt {1-2 x}+\frac {4671}{32} (1-2 x)^{3/2}-\frac {405}{32} (1-2 x)^{5/2}\right ) \, dx\\ &=\frac {26411}{96 (1-2 x)^{3/2}}-\frac {57281}{32 \sqrt {1-2 x}}-\frac {24843}{16} \sqrt {1-2 x}+\frac {3591}{16} (1-2 x)^{3/2}-\frac {4671}{160} (1-2 x)^{5/2}+\frac {405}{224} (1-2 x)^{7/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 38, normalized size = 0.48 \[ -\frac {6075 x^5+33858 x^4+105624 x^3+435312 x^2-909264 x+301408}{105 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 46, normalized size = 0.58 \[ -\frac {{\left (6075 \, x^{5} + 33858 \, x^{4} + 105624 \, x^{3} + 435312 \, x^{2} - 909264 \, x + 301408\right )} \sqrt {-2 \, x + 1}}{105 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.21, size = 72, normalized size = 0.91 \[ -\frac {405}{224} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {4671}{160} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {3591}{16} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {24843}{16} \, \sqrt {-2 \, x + 1} - \frac {343 \, {\left (501 \, x - 212\right )}}{48 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.44 \[ -\frac {6075 x^{5}+33858 x^{4}+105624 x^{3}+435312 x^{2}-909264 x +301408}{105 \left (-2 x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 51, normalized size = 0.65 \[ \frac {405}{224} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {4671}{160} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {3591}{16} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {24843}{16} \, \sqrt {-2 \, x + 1} + \frac {343 \, {\left (501 \, x - 212\right )}}{48 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 50, normalized size = 0.63 \[ \frac {\frac {57281\,x}{16}-\frac {18179}{12}}{{\left (1-2\,x\right )}^{3/2}}-\frac {24843\,\sqrt {1-2\,x}}{16}+\frac {3591\,{\left (1-2\,x\right )}^{3/2}}{16}-\frac {4671\,{\left (1-2\,x\right )}^{5/2}}{160}+\frac {405\,{\left (1-2\,x\right )}^{7/2}}{224} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 30.35, size = 70, normalized size = 0.89 \[ \frac {405 \left (1 - 2 x\right )^{\frac {7}{2}}}{224} - \frac {4671 \left (1 - 2 x\right )^{\frac {5}{2}}}{160} + \frac {3591 \left (1 - 2 x\right )^{\frac {3}{2}}}{16} - \frac {24843 \sqrt {1 - 2 x}}{16} - \frac {57281}{32 \sqrt {1 - 2 x}} + \frac {26411}{96 \left (1 - 2 x\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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