Optimal. Leaf size=53 \[ \frac {25}{8} (1-2 x)^{3/2}-\frac {505}{8} \sqrt {1-2 x}-\frac {1133}{8 \sqrt {1-2 x}}+\frac {847}{24 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.01, antiderivative size = 53, 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 {25}{8} (1-2 x)^{3/2}-\frac {505}{8} \sqrt {1-2 x}-\frac {1133}{8 \sqrt {1-2 x}}+\frac {847}{24 (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)^2}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {847}{8 (1-2 x)^{5/2}}-\frac {1133}{8 (1-2 x)^{3/2}}+\frac {505}{8 \sqrt {1-2 x}}-\frac {75}{8} \sqrt {1-2 x}\right ) \, dx\\ &=\frac {847}{24 (1-2 x)^{3/2}}-\frac {1133}{8 \sqrt {1-2 x}}-\frac {505}{8} \sqrt {1-2 x}+\frac {25}{8} (1-2 x)^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.53 \begin {gather*} -\frac {75 x^3+645 x^2-1551 x+499}{3 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 40, normalized size = 0.75 \begin {gather*} \frac {75 (1-2 x)^3-1515 (1-2 x)^2-3399 (1-2 x)+847}{24 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.13, size = 36, normalized size = 0.68 \begin {gather*} -\frac {{\left (75 \, x^{3} + 645 \, x^{2} - 1551 \, x + 499\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 = 1.20, size = 40, normalized size = 0.75 \begin {gather*} \frac {25}{8} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {505}{8} \, \sqrt {-2 \, x + 1} - \frac {11 \, {\left (309 \, x - 116\right )}}{12 \, {\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 = 25, normalized size = 0.47 \begin {gather*} -\frac {75 x^{3}+645 x^{2}-1551 x +499}{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 = 0.55, size = 33, normalized size = 0.62 \begin {gather*} \frac {25}{8} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {505}{8} \, \sqrt {-2 \, x + 1} + \frac {11 \, {\left (309 \, x - 116\right )}}{12 \, {\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 = 1.19, size = 38, normalized size = 0.72 \begin {gather*} \frac {1515\,{\left (2\,x-1\right )}^2-6798\,x+75\,{\left (2\,x-1\right )}^3+2552}{\sqrt {1-2\,x}\,\left (48\,x-24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.69, size = 102, normalized size = 1.92 \begin {gather*} \frac {75 x^{3}}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} + \frac {645 x^{2}}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} - \frac {1551 x}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} + \frac {499}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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