Optimal. Leaf size=40 \[ -\frac{9}{4 \sqrt{2 x-1}}+\frac{7}{2 (2 x-1)^{3/2}}-\frac{49}{20 (2 x-1)^{5/2}} \]
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Rubi [A] time = 0.0074687, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {43} \[ -\frac{9}{4 \sqrt{2 x-1}}+\frac{7}{2 (2 x-1)^{3/2}}-\frac{49}{20 (2 x-1)^{5/2}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(-5+3 x)^2}{(-1+2 x)^{7/2}} \, dx &=\int \left (\frac{49}{4 (-1+2 x)^{7/2}}-\frac{21}{2 (-1+2 x)^{5/2}}+\frac{9}{4 (-1+2 x)^{3/2}}\right ) \, dx\\ &=-\frac{49}{20 (-1+2 x)^{5/2}}+\frac{7}{2 (-1+2 x)^{3/2}}-\frac{9}{4 \sqrt{-1+2 x}}\\ \end{align*}
Mathematica [A] time = 0.0117336, size = 23, normalized size = 0.57 \[ \frac{-45 x^2+80 x-41}{5 (2 x-1)^{5/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 20, normalized size = 0.5 \begin{align*} -{\frac{45\,{x}^{2}-80\,x+41}{5} \left ( 2\,x-1 \right ) ^{-{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.921544, size = 31, normalized size = 0.78 \begin{align*} -\frac{45 \,{\left (2 \, x - 1\right )}^{2} - 140 \, x + 119}{20 \,{\left (2 \, x - 1\right )}^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83398, size = 92, normalized size = 2.3 \begin{align*} -\frac{{\left (45 \, x^{2} - 80 \, x + 41\right )} \sqrt{2 \, x - 1}}{5 \,{\left (8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.35946, size = 116, normalized size = 2.9 \begin{align*} - \frac{45 x^{2}}{20 x^{2} \sqrt{2 x - 1} - 20 x \sqrt{2 x - 1} + 5 \sqrt{2 x - 1}} + \frac{80 x}{20 x^{2} \sqrt{2 x - 1} - 20 x \sqrt{2 x - 1} + 5 \sqrt{2 x - 1}} - \frac{41}{20 x^{2} \sqrt{2 x - 1} - 20 x \sqrt{2 x - 1} + 5 \sqrt{2 x - 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12353, size = 31, normalized size = 0.78 \begin{align*} -\frac{45 \,{\left (2 \, x - 1\right )}^{2} - 140 \, x + 119}{20 \,{\left (2 \, x - 1\right )}^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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