Optimal. Leaf size=38 \[ -\frac {15}{4} \sqrt {1-2 x}-\frac {17}{\sqrt {1-2 x}}+\frac {77}{12 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.01, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {15}{4} \sqrt {1-2 x}-\frac {17}{\sqrt {1-2 x}}+\frac {77}{12 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {77}{4 (1-2 x)^{5/2}}-\frac {17}{(1-2 x)^{3/2}}+\frac {15}{4 \sqrt {1-2 x}}\right ) \, dx\\ &=\frac {77}{12 (1-2 x)^{3/2}}-\frac {17}{\sqrt {1-2 x}}-\frac {15}{4} \sqrt {1-2 x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.61 \[ -\frac {45 x^2-147 x+43}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 31, normalized size = 0.82 \[ -\frac {{\left (45 \, x^{2} - 147 \, x + 43\right )} \sqrt {-2 \, x + 1}}{3 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 31, normalized size = 0.82 \[ -\frac {15}{4} \, \sqrt {-2 \, x + 1} - \frac {408 \, x - 127}{12 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.53 \[ -\frac {45 x^{2}-147 x +43}{3 \left (-2 x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 24, normalized size = 0.63 \[ -\frac {15}{4} \, \sqrt {-2 \, x + 1} + \frac {408 \, x - 127}{12 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.22, size = 29, normalized size = 0.76 \[ \frac {45\,{\left (2\,x-1\right )}^2-408\,x+127}{\sqrt {1-2\,x}\,\left (24\,x-12\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.66, size = 75, normalized size = 1.97 \[ \frac {45 x^{2}}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} - \frac {147 x}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} + \frac {43}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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