Optimal. Leaf size=82 \[ -\frac {a^6 c^5}{9 x^9}+\frac {a^5 b c^5}{2 x^8}-\frac {5 a^4 b^2 c^5}{7 x^7}+\frac {a^2 b^4 c^5}{x^5}-\frac {a b^5 c^5}{x^4}+\frac {b^6 c^5}{3 x^3} \]
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Rubi [A] time = 0.04, antiderivative size = 82, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {75} \[ -\frac {5 a^4 b^2 c^5}{7 x^7}+\frac {a^2 b^4 c^5}{x^5}+\frac {a^5 b c^5}{2 x^8}-\frac {a^6 c^5}{9 x^9}-\frac {a b^5 c^5}{x^4}+\frac {b^6 c^5}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 75
Rubi steps
\begin {align*} \int \frac {(a+b x) (a c-b c x)^5}{x^{10}} \, dx &=\int \left (\frac {a^6 c^5}{x^{10}}-\frac {4 a^5 b c^5}{x^9}+\frac {5 a^4 b^2 c^5}{x^8}-\frac {5 a^2 b^4 c^5}{x^6}+\frac {4 a b^5 c^5}{x^5}-\frac {b^6 c^5}{x^4}\right ) \, dx\\ &=-\frac {a^6 c^5}{9 x^9}+\frac {a^5 b c^5}{2 x^8}-\frac {5 a^4 b^2 c^5}{7 x^7}+\frac {a^2 b^4 c^5}{x^5}-\frac {a b^5 c^5}{x^4}+\frac {b^6 c^5}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 68, normalized size = 0.83 \[ c^5 \left (-\frac {a^6}{9 x^9}+\frac {a^5 b}{2 x^8}-\frac {5 a^4 b^2}{7 x^7}+\frac {a^2 b^4}{x^5}-\frac {a b^5}{x^4}+\frac {b^6}{3 x^3}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 75, normalized size = 0.91 \[ \frac {42 \, b^{6} c^{5} x^{6} - 126 \, a b^{5} c^{5} x^{5} + 126 \, a^{2} b^{4} c^{5} x^{4} - 90 \, a^{4} b^{2} c^{5} x^{2} + 63 \, a^{5} b c^{5} x - 14 \, a^{6} c^{5}}{126 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.83, size = 75, normalized size = 0.91 \[ \frac {42 \, b^{6} c^{5} x^{6} - 126 \, a b^{5} c^{5} x^{5} + 126 \, a^{2} b^{4} c^{5} x^{4} - 90 \, a^{4} b^{2} c^{5} x^{2} + 63 \, a^{5} b c^{5} x - 14 \, a^{6} c^{5}}{126 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 61, normalized size = 0.74 \[ \left (\frac {b^{6}}{3 x^{3}}-\frac {a \,b^{5}}{x^{4}}+\frac {a^{2} b^{4}}{x^{5}}-\frac {5 a^{4} b^{2}}{7 x^{7}}+\frac {a^{5} b}{2 x^{8}}-\frac {a^{6}}{9 x^{9}}\right ) c^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.12, size = 75, normalized size = 0.91 \[ \frac {42 \, b^{6} c^{5} x^{6} - 126 \, a b^{5} c^{5} x^{5} + 126 \, a^{2} b^{4} c^{5} x^{4} - 90 \, a^{4} b^{2} c^{5} x^{2} + 63 \, a^{5} b c^{5} x - 14 \, a^{6} c^{5}}{126 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 74, normalized size = 0.90 \[ -\frac {\frac {a^6\,c^5}{9}-\frac {a^5\,b\,c^5\,x}{2}+\frac {5\,a^4\,b^2\,c^5\,x^2}{7}-a^2\,b^4\,c^5\,x^4+a\,b^5\,c^5\,x^5-\frac {b^6\,c^5\,x^6}{3}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.52, size = 82, normalized size = 1.00 \[ - \frac {14 a^{6} c^{5} - 63 a^{5} b c^{5} x + 90 a^{4} b^{2} c^{5} x^{2} - 126 a^{2} b^{4} c^{5} x^{4} + 126 a b^{5} c^{5} x^{5} - 42 b^{6} c^{5} x^{6}}{126 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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