Optimal. Leaf size=37 \[ -\frac{2 (A c+b B)}{3 x^{3/2}}-\frac{2 A b}{5 x^{5/2}}-\frac{2 B c}{\sqrt{x}} \]
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Rubi [A] time = 0.0169217, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {765} \[ -\frac{2 (A c+b B)}{3 x^{3/2}}-\frac{2 A b}{5 x^{5/2}}-\frac{2 B c}{\sqrt{x}} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (b x+c x^2\right )}{x^{9/2}} \, dx &=\int \left (\frac{A b}{x^{7/2}}+\frac{b B+A c}{x^{5/2}}+\frac{B c}{x^{3/2}}\right ) \, dx\\ &=-\frac{2 A b}{5 x^{5/2}}-\frac{2 (b B+A c)}{3 x^{3/2}}-\frac{2 B c}{\sqrt{x}}\\ \end{align*}
Mathematica [A] time = 0.0099976, size = 30, normalized size = 0.81 \[ -\frac{2 (A (3 b+5 c x)+5 B x (b+3 c x))}{15 x^{5/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 28, normalized size = 0.8 \begin{align*} -{\frac{30\,Bc{x}^{2}+10\,Acx+10\,bBx+6\,Ab}{15}{x}^{-{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06149, size = 36, normalized size = 0.97 \begin{align*} -\frac{2 \,{\left (15 \, B c x^{2} + 3 \, A b + 5 \,{\left (B b + A c\right )} x\right )}}{15 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78538, size = 73, normalized size = 1.97 \begin{align*} -\frac{2 \,{\left (15 \, B c x^{2} + 3 \, A b + 5 \,{\left (B b + A c\right )} x\right )}}{15 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.37419, size = 46, normalized size = 1.24 \begin{align*} - \frac{2 A b}{5 x^{\frac{5}{2}}} - \frac{2 A c}{3 x^{\frac{3}{2}}} - \frac{2 B b}{3 x^{\frac{3}{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 = 1.12486, size = 36, normalized size = 0.97 \begin{align*} -\frac{2 \,{\left (15 \, B c x^{2} + 5 \, B b x + 5 \, A c x + 3 \, A b\right )}}{15 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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