Optimal. Leaf size=66 \[ -\frac {75}{16} (1-2 x)^{5/2}+\frac {1675}{24} (1-2 x)^{3/2}-\frac {2805}{4} \sqrt {1-2 x}-\frac {8349}{8 \sqrt {1-2 x}}+\frac {9317}{48 (1-2 x)^{3/2}} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \begin {gather*} -\frac {75}{16} (1-2 x)^{5/2}+\frac {1675}{24} (1-2 x)^{3/2}-\frac {2805}{4} \sqrt {1-2 x}-\frac {8349}{8 \sqrt {1-2 x}}+\frac {9317}{48 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)^3}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {9317}{16 (1-2 x)^{5/2}}-\frac {8349}{8 (1-2 x)^{3/2}}+\frac {2805}{4 \sqrt {1-2 x}}-\frac {1675}{8} \sqrt {1-2 x}+\frac {375}{16} (1-2 x)^{3/2}\right ) \, dx\\ &=\frac {9317}{48 (1-2 x)^{3/2}}-\frac {8349}{8 \sqrt {1-2 x}}-\frac {2805}{4} \sqrt {1-2 x}+\frac {1675}{24} (1-2 x)^{3/2}-\frac {75}{16} (1-2 x)^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} -\frac {225 x^4+1225 x^3+6240 x^2-13533 x+4457}{3 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 49, normalized size = 0.74 \begin {gather*} \frac {-225 (1-2 x)^4+3350 (1-2 x)^3-33660 (1-2 x)^2-50094 (1-2 x)+9317}{48 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 41, normalized size = 0.62 \begin {gather*} -\frac {{\left (225 \, x^{4} + 1225 \, x^{3} + 6240 \, x^{2} - 13533 \, x + 4457\right )} \sqrt {-2 \, x + 1}}{3 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 56, normalized size = 0.85 \begin {gather*} -\frac {75}{16} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {1675}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {2805}{4} \, \sqrt {-2 \, x + 1} - \frac {121 \, {\left (828 \, x - 337\right )}}{48 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \end {gather*}
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 \begin {gather*} -\frac {225 x^{4}+1225 x^{3}+6240 x^{2}-13533 x +4457}{3 \left (-2 x +1\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 42, normalized size = 0.64 \begin {gather*} -\frac {75}{16} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {1675}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {2805}{4} \, \sqrt {-2 \, x + 1} + \frac {121 \, {\left (828 \, x - 337\right )}}{48 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \end {gather*}
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 \begin {gather*} \frac {\frac {8349\,x}{4}-\frac {40777}{48}}{{\left (1-2\,x\right )}^{3/2}}-\frac {2805\,\sqrt {1-2\,x}}{4}+\frac {1675\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {75\,{\left (1-2\,x\right )}^{5/2}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 23.39, size = 58, normalized size = 0.88 \begin {gather*} - \frac {75 \left (1 - 2 x\right )^{\frac {5}{2}}}{16} + \frac {1675 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} - \frac {2805 \sqrt {1 - 2 x}}{4} - \frac {8349}{8 \sqrt {1 - 2 x}} + \frac {9317}{48 \left (1 - 2 x\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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