Optimal. Leaf size=15 \[ \frac{1}{2 b (a-b x)^2} \]
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Rubi [A] time = 0.0066662, antiderivative size = 15, 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, 32} \[ \frac{1}{2 b (a-b x)^2} \]
Antiderivative was successfully verified.
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Rule 627
Rule 32
Rubi steps
\begin{align*} \int \frac{(a+b x)^3}{\left (a^2-b^2 x^2\right )^3} \, dx &=\int \frac{1}{(a-b x)^3} \, dx\\ &=\frac{1}{2 b (a-b x)^2}\\ \end{align*}
Mathematica [A] time = 0.001539, size = 15, normalized size = 1. \[ \frac{1}{2 b (a-b x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.039, size = 15, normalized size = 1. \begin{align*}{\frac{1}{2\,b \left ( bx-a \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02489, size = 32, normalized size = 2.13 \begin{align*} \frac{1}{2 \,{\left (b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6542, size = 47, normalized size = 3.13 \begin{align*} \frac{1}{2 \,{\left (b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.347631, size = 24, normalized size = 1.6 \begin{align*} \frac{1}{2 a^{2} b - 4 a b^{2} x + 2 b^{3} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19786, size = 19, normalized size = 1.27 \begin{align*} \frac{1}{2 \,{\left (b x - a\right )}^{2} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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