Optimal. Leaf size=27 \[ \frac {11}{6 (1-2 x)^{3/2}}-\frac {5}{2 \sqrt {1-2 x}} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \[ \frac {11}{6 (1-2 x)^{3/2}}-\frac {5}{2 \sqrt {1-2 x}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac {11}{2 (1-2 x)^{5/2}}-\frac {5}{2 (1-2 x)^{3/2}}\right ) \, dx\\ &=\frac {11}{6 (1-2 x)^{3/2}}-\frac {5}{2 \sqrt {1-2 x}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.67 \[ \frac {15 x-2}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.96, size = 26, normalized size = 0.96 \[ \frac {{\left (15 \, x - 2\right )} \sqrt {-2 \, x + 1}}{3 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 21, normalized size = 0.78 \[ -\frac {15 \, x - 2}{3 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \[ \frac {15 x -2}{3 \left (-2 x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 14, normalized size = 0.52 \[ \frac {15 \, x - 2}{3 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.48 \[ \frac {5\,x-\frac {2}{3}}{{\left (1-2\,x\right )}^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.59, size = 48, normalized size = 1.78 \[ - \frac {15 x}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} + \frac {2}{6 x \sqrt {1 - 2 x} - 3 \sqrt {1 - 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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