Optimal. Leaf size=14 \[ -\frac{1}{2 d (c+d x)^2} \]
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Rubi [A] time = 0.0017357, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ -\frac{1}{2 d (c+d x)^2} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int \frac{1}{(c+d x)^3} \, dx &=-\frac{1}{2 d (c+d x)^2}\\ \end{align*}
Mathematica [A] time = 0.0024733, size = 14, normalized size = 1. \[ -\frac{1}{2 d (c+d x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 13, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,d \left ( dx+c \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.957684, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{2 \,{\left (d x + c\right )}^{2} d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.62047, size = 49, normalized size = 3.5 \begin{align*} -\frac{1}{2 \,{\left (d^{3} x^{2} + 2 \, c d^{2} x + c^{2} d\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.30866, size = 26, normalized size = 1.86 \begin{align*} - \frac{1}{2 c^{2} d + 4 c d^{2} x + 2 d^{3} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07505, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{2 \,{\left (d x + c\right )}^{2} d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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