Optimal. Leaf size=10 \[ \frac{x}{(a-b x)^2} \]
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Rubi [A] time = 0.0070928, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {627, 34} \[ \frac{x}{(a-b x)^2} \]
Antiderivative was successfully verified.
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Rule 627
Rule 34
Rubi steps
\begin{align*} \int \frac{(a+b x)^4}{\left (a^2-b^2 x^2\right )^3} \, dx &=\int \frac{a+b x}{(a-b x)^3} \, dx\\ &=\frac{x}{(a-b x)^2}\\ \end{align*}
Mathematica [A] time = 0.0035456, size = 10, normalized size = 1. \[ \frac{x}{(a-b x)^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.044, size = 29, normalized size = 2.9 \begin{align*}{\frac{a}{b \left ( bx-a \right ) ^{2}}}+{\frac{1}{b \left ( bx-a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00771, size = 27, normalized size = 2.7 \begin{align*} \frac{x}{b^{2} x^{2} - 2 \, a b x + a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.65899, size = 39, normalized size = 3.9 \begin{align*} \frac{x}{b^{2} x^{2} - 2 \, a b x + a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.357719, size = 17, normalized size = 1.7 \begin{align*} \frac{x}{a^{2} - 2 a b x + b^{2} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19041, size = 15, normalized size = 1.5 \begin{align*} \frac{x}{{\left (b x - a\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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