Optimal. Leaf size=18 \[ -\frac{c^5 (a-b x)^6}{3 x^3} \]
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Rubi [A] time = 0.0024814, 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} \[ -\frac{c^5 (a-b x)^6}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 74
Rubi steps
\begin{align*} \int \frac{(a+b x) (a c-b c x)^5}{x^4} \, dx &=-\frac{c^5 (a-b x)^6}{3 x^3}\\ \end{align*}
Mathematica [B] time = 0.0064213, size = 63, normalized size = 3.5 \[ c^5 \left (-\frac{5 a^4 b^2}{x}-5 a^2 b^4 x+\frac{2 a^5 b}{x^2}-\frac{a^6}{3 x^3}+2 a b^5 x^2-\frac{b^6 x^3}{3}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.006, size = 60, normalized size = 3.3 \begin{align*}{c}^{5} \left ( -{\frac{{b}^{6}{x}^{3}}{3}}+2\,a{b}^{5}{x}^{2}-5\,{a}^{2}{b}^{4}x-{\frac{{a}^{6}}{3\,{x}^{3}}}+2\,{\frac{{a}^{5}b}{{x}^{2}}}-5\,{\frac{{a}^{4}{b}^{2}}{x}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.06496, size = 99, normalized size = 5.5 \begin{align*} -\frac{1}{3} \, b^{6} c^{5} x^{3} + 2 \, a b^{5} c^{5} x^{2} - 5 \, a^{2} b^{4} c^{5} x - \frac{15 \, a^{4} b^{2} c^{5} x^{2} - 6 \, a^{5} b c^{5} x + a^{6} c^{5}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.69138, size = 149, normalized size = 8.28 \begin{align*} -\frac{b^{6} c^{5} x^{6} - 6 \, a b^{5} c^{5} x^{5} + 15 \, a^{2} b^{4} c^{5} x^{4} + 15 \, a^{4} b^{2} c^{5} x^{2} - 6 \, a^{5} b c^{5} x + a^{6} c^{5}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.412067, size = 76, normalized size = 4.22 \begin{align*} - 5 a^{2} b^{4} c^{5} x + 2 a b^{5} c^{5} x^{2} - \frac{b^{6} c^{5} x^{3}}{3} - \frac{a^{6} c^{5} - 6 a^{5} b c^{5} x + 15 a^{4} b^{2} c^{5} x^{2}}{3 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.32583, size = 99, normalized size = 5.5 \begin{align*} -\frac{1}{3} \, b^{6} c^{5} x^{3} + 2 \, a b^{5} c^{5} x^{2} - 5 \, a^{2} b^{4} c^{5} x - \frac{15 \, a^{4} b^{2} c^{5} x^{2} - 6 \, a^{5} b c^{5} x + a^{6} c^{5}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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