Optimal. Leaf size=43 \[ -\frac{2 a A}{7 x^{7/2}}-\frac{2 a B}{5 x^{5/2}}-\frac{2 A c}{3 x^{3/2}}-\frac{2 B c}{\sqrt{x}} \]
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Rubi [A] time = 0.0120947, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {766} \[ -\frac{2 a A}{7 x^{7/2}}-\frac{2 a B}{5 x^{5/2}}-\frac{2 A c}{3 x^{3/2}}-\frac{2 B c}{\sqrt{x}} \]
Antiderivative was successfully verified.
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Rule 766
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (a+c x^2\right )}{x^{9/2}} \, dx &=\int \left (\frac{a A}{x^{9/2}}+\frac{a B}{x^{7/2}}+\frac{A c}{x^{5/2}}+\frac{B c}{x^{3/2}}\right ) \, dx\\ &=-\frac{2 a A}{7 x^{7/2}}-\frac{2 a B}{5 x^{5/2}}-\frac{2 A c}{3 x^{3/2}}-\frac{2 B c}{\sqrt{x}}\\ \end{align*}
Mathematica [A] time = 0.0146186, size = 33, normalized size = 0.77 \[ \frac{-6 a (5 A+7 B x)-70 c x^2 (A+3 B x)}{105 x^{7/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.7 \begin{align*} -{\frac{210\,Bc{x}^{3}+70\,Ac{x}^{2}+42\,aBx+30\,aA}{105}{x}^{-{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00226, size = 39, normalized size = 0.91 \begin{align*} -\frac{2 \,{\left (105 \, B c x^{3} + 35 \, A c x^{2} + 21 \, B a x + 15 \, A a\right )}}{105 \, x^{\frac{7}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28399, size = 85, normalized size = 1.98 \begin{align*} -\frac{2 \,{\left (105 \, B c x^{3} + 35 \, A c x^{2} + 21 \, B a x + 15 \, A a\right )}}{105 \, x^{\frac{7}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 4.12499, size = 46, normalized size = 1.07 \begin{align*} - \frac{2 A a}{7 x^{\frac{7}{2}}} - \frac{2 A c}{3 x^{\frac{3}{2}}} - \frac{2 B a}{5 x^{\frac{5}{2}}} - \frac{2 B c}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.32025, size = 39, normalized size = 0.91 \begin{align*} -\frac{2 \,{\left (105 \, B c x^{3} + 35 \, A c x^{2} + 21 \, B a x + 15 \, A a\right )}}{105 \, x^{\frac{7}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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