Optimal. Leaf size=18 \[ -\frac {c^5 (a-b x)^6}{3 x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {74} \begin {gather*} -\frac {c^5 (a-b x)^6}{3 x^3} \end {gather*}
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*}
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Mathematica [B] time = 0.02, size = 63, normalized size = 3.50 \begin {gather*} c^5 \left (-\frac {a^6}{3 x^3}+\frac {2 a^5 b}{x^2}-\frac {5 a^4 b^2}{x}-5 a^2 b^4 x+2 a b^5 x^2-\frac {b^6 x^3}{3}\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x) (a c-b c x)^5}{x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.12, size = 73, normalized size = 4.06 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.04, size = 73, normalized size = 4.06 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 60, normalized size = 3.33 \begin {gather*} \left (-\frac {b^{6} x^{3}}{3}+2 a \,b^{5} x^{2}-5 a^{2} b^{4} x -\frac {5 a^{4} b^{2}}{x}+\frac {2 a^{5} b}{x^{2}}-\frac {a^{6}}{3 x^{3}}\right ) c^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.04, size = 73, normalized size = 4.06 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 74, normalized size = 4.11 \begin {gather*} 2\,a\,b^5\,c^5\,x^2-\frac {b^6\,c^5\,x^3}{3}-5\,a^2\,b^4\,c^5\,x-\frac {\frac {a^6\,c^5}{3}-2\,a^5\,b\,c^5\,x+5\,a^4\,b^2\,c^5\,x^2}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.24, size = 76, normalized size = 4.22 \begin {gather*} - 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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