Optimal. Leaf size=66 \[ -\frac {45}{16} (1-2 x)^{5/2}+\frac {85}{2} (1-2 x)^{3/2}-\frac {3467}{8} \sqrt {1-2 x}-\frac {1309}{2 \sqrt {1-2 x}}+\frac {5929}{48 (1-2 x)^{3/2}} \]
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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} \[ -\frac {45}{16} (1-2 x)^{5/2}+\frac {85}{2} (1-2 x)^{3/2}-\frac {3467}{8} \sqrt {1-2 x}-\frac {1309}{2 \sqrt {1-2 x}}+\frac {5929}{48 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {5929}{16 (1-2 x)^{5/2}}-\frac {1309}{2 (1-2 x)^{3/2}}+\frac {3467}{8 \sqrt {1-2 x}}-\frac {255}{2} \sqrt {1-2 x}+\frac {225}{16} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac {5929}{48 (1-2 x)^{3/2}}-\frac {1309}{2 \sqrt {1-2 x}}-\frac {3467}{8} \sqrt {1-2 x}+\frac {85}{2} (1-2 x)^{3/2}-\frac {45}{16} (1-2 x)^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \[ -\frac {135 x^4+750 x^3+3873 x^2-8430 x+2774}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 41, normalized size = 0.62 \[ -\frac {{\left (135 \, x^{4} + 750 \, x^{3} + 3873 \, x^{2} - 8430 \, x + 2774\right )} \sqrt {-2 \, x + 1}}{3 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 56, normalized size = 0.85 \[ -\frac {45}{16} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {85}{2} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {3467}{8} \, \sqrt {-2 \, x + 1} - \frac {77 \, {\left (816 \, x - 331\right )}}{48 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 0.45 \[ -\frac {135 x^{4}+750 x^{3}+3873 x^{2}-8430 x +2774}{3 \left (-2 x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 42, normalized size = 0.64 \[ -\frac {45}{16} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {85}{2} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {3467}{8} \, \sqrt {-2 \, x + 1} + \frac {77 \, {\left (816 \, x - 331\right )}}{48 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 41, normalized size = 0.62 \[ \frac {1309\,x-\frac {25487}{48}}{{\left (1-2\,x\right )}^{3/2}}-\frac {3467\,\sqrt {1-2\,x}}{8}+\frac {85\,{\left (1-2\,x\right )}^{3/2}}{2}-\frac {45\,{\left (1-2\,x\right )}^{5/2}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 22.47, size = 58, normalized size = 0.88 \[ - \frac {45 \left (1 - 2 x\right )^{\frac {5}{2}}}{16} + \frac {85 \left (1 - 2 x\right )^{\frac {3}{2}}}{2} - \frac {3467 \sqrt {1 - 2 x}}{8} - \frac {1309}{2 \sqrt {1 - 2 x}} + \frac {5929}{48 \left (1 - 2 x\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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