Optimal. Leaf size=18 \[ -\frac{c^3 (a-b x)^4}{2 x^2} \]
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Rubi [A] time = 0.0029245, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {74} \[ -\frac{c^3 (a-b x)^4}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 74
Rubi steps
\begin{align*} \int \frac{(a+b x) (a c-b c x)^3}{x^3} \, dx &=-\frac{c^3 (a-b x)^4}{2 x^2}\\ \end{align*}
Mathematica [B] time = 0.0066017, size = 41, normalized size = 2.28 \[ c^3 \left (\frac{2 a^3 b}{x}-\frac{a^4}{2 x^2}+2 a b^3 x-\frac{b^4 x^2}{2}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.004, size = 38, normalized size = 2.1 \begin{align*}{c}^{3} \left ( -{\frac{{b}^{4}{x}^{2}}{2}}+2\,a{b}^{3}x-{\frac{{a}^{4}}{2\,{x}^{2}}}+2\,{\frac{{a}^{3}b}{x}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.01585, size = 62, normalized size = 3.44 \begin{align*} -\frac{1}{2} \, b^{4} c^{3} x^{2} + 2 \, a b^{3} c^{3} x + \frac{4 \, a^{3} b c^{3} x - a^{4} c^{3}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.82898, size = 92, normalized size = 5.11 \begin{align*} -\frac{b^{4} c^{3} x^{4} - 4 \, a b^{3} c^{3} x^{3} - 4 \, a^{3} b c^{3} x + a^{4} c^{3}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.31966, size = 46, normalized size = 2.56 \begin{align*} 2 a b^{3} c^{3} x - \frac{b^{4} c^{3} x^{2}}{2} + \frac{- a^{4} c^{3} + 4 a^{3} b c^{3} x}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.19523, size = 62, normalized size = 3.44 \begin{align*} -\frac{1}{2} \, b^{4} c^{3} x^{2} + 2 \, a b^{3} c^{3} x + \frac{4 \, a^{3} b c^{3} x - a^{4} c^{3}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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