Optimal. Leaf size=13 \[ \frac {x}{c^3 (a-b x)^2} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {34} \[ \frac {x}{c^3 (a-b x)^2} \]
Antiderivative was successfully verified.
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Rule 34
Rubi steps
\begin {align*} \int \frac {a+b x}{(a c-b c x)^3} \, dx &=\frac {x}{c^3 (a-b x)^2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 1.00 \[ \frac {x}{c^3 (a-b x)^2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 30, normalized size = 2.31 \[ \frac {x}{b^{2} c^{3} x^{2} - 2 \, a b c^{3} x + a^{2} c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 14, normalized size = 1.08 \[ \frac {x}{{\left (b x - a\right )}^{2} c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 33, normalized size = 2.54 \[ \frac {\frac {a}{\left (b x -a \right )^{2} b}+\frac {1}{\left (b x -a \right ) b}}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.31, size = 30, normalized size = 2.31 \[ \frac {x}{b^{2} c^{3} x^{2} - 2 \, a b c^{3} x + a^{2} c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 13, normalized size = 1.00 \[ \frac {x}{c^3\,{\left (a-b\,x\right )}^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.24, size = 27, normalized size = 2.08 \[ \frac {x}{a^{2} c^{3} - 2 a b c^{3} x + b^{2} c^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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