Optimal. Leaf size=38 \[ \frac {2 a}{5 b c^6 (a-b x)^5}-\frac {1}{4 b c^6 (a-b x)^4} \]
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Rubi [A] time = 0.02, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {43} \[ \frac {2 a}{5 b c^6 (a-b x)^5}-\frac {1}{4 b c^6 (a-b x)^4} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{(a c-b c x)^6} \, dx &=\int \left (\frac {2 a}{c^6 (a-b x)^6}-\frac {1}{c^6 (a-b x)^5}\right ) \, dx\\ &=\frac {2 a}{5 b c^6 (a-b x)^5}-\frac {1}{4 b c^6 (a-b x)^4}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 0.71 \[ -\frac {3 a+5 b x}{20 b c^6 (b x-a)^5} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.45, size = 84, normalized size = 2.21 \[ -\frac {5 \, b x + 3 \, a}{20 \, {\left (b^{6} c^{6} x^{5} - 5 \, a b^{5} c^{6} x^{4} + 10 \, a^{2} b^{4} c^{6} x^{3} - 10 \, a^{3} b^{3} c^{6} x^{2} + 5 \, a^{4} b^{2} c^{6} x - a^{5} b c^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 25, normalized size = 0.66 \[ -\frac {5 \, b x + 3 \, a}{20 \, {\left (b x - a\right )}^{5} b c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.92 \[ \frac {-\frac {2 a}{5 \left (b x -a \right )^{5} b}-\frac {1}{4 \left (b x -a \right )^{4} b}}{c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.31, size = 84, normalized size = 2.21 \[ -\frac {5 \, b x + 3 \, a}{20 \, {\left (b^{6} c^{6} x^{5} - 5 \, a b^{5} c^{6} x^{4} + 10 \, a^{2} b^{4} c^{6} x^{3} - 10 \, a^{3} b^{3} c^{6} x^{2} + 5 \, a^{4} b^{2} c^{6} x - a^{5} b c^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 82, normalized size = 2.16 \[ \frac {\frac {x}{4}+\frac {3\,a}{20\,b}}{a^5\,c^6-5\,a^4\,b\,c^6\,x+10\,a^3\,b^2\,c^6\,x^2-10\,a^2\,b^3\,c^6\,x^3+5\,a\,b^4\,c^6\,x^4-b^5\,c^6\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.46, size = 88, normalized size = 2.32 \[ \frac {- 3 a - 5 b x}{- 20 a^{5} b c^{6} + 100 a^{4} b^{2} c^{6} x - 200 a^{3} b^{3} c^{6} x^{2} + 200 a^{2} b^{4} c^{6} x^{3} - 100 a b^{5} c^{6} x^{4} + 20 b^{6} c^{6} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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