Optimal. Leaf size=13 \[ \frac{x}{c^3 (a-b x)^2} \]
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Rubi [A] time = 0.0021911, antiderivative size = 13, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0078797, size = 13, normalized size = 1. \[ \frac{x}{c^3 (a-b x)^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.003, size = 33, normalized size = 2.5 \begin{align*}{\frac{1}{{c}^{3}} \left ({\frac{1}{b \left ( bx-a \right ) }}+{\frac{a}{b \left ( bx-a \right ) ^{2}}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.989695, size = 41, normalized size = 3.15 \begin{align*} \frac{x}{b^{2} c^{3} x^{2} - 2 \, a b c^{3} x + a^{2} c^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.48136, size = 55, normalized size = 4.23 \begin{align*} \frac{x}{b^{2} c^{3} x^{2} - 2 \, a b c^{3} x + a^{2} c^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.368923, size = 27, normalized size = 2.08 \begin{align*} \frac{x}{a^{2} c^{3} - 2 a b c^{3} x + b^{2} c^{3} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05118, size = 19, normalized size = 1.46 \begin{align*} \frac{x}{{\left (b x - a\right )}^{2} c^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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