Optimal. Leaf size=10 \[ -\frac{1}{2 d x^2} \]
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Rubi [A] time = 0.0014073, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {12, 30} \[ -\frac{1}{2 d x^2} \]
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{d x^3} \, dx &=\frac{\int \frac{1}{x^3} \, dx}{d}\\ &=-\frac{1}{2 d x^2}\\ \end{align*}
Mathematica [A] time = 0.0003004, size = 10, normalized size = 1. \[ -\frac{1}{2 d x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 9, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,d{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00634, size = 11, normalized size = 1.1 \begin{align*} -\frac{1}{2 \, d x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49792, size = 19, normalized size = 1.9 \begin{align*} -\frac{1}{2 \, d x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062868, size = 8, normalized size = 0.8 \begin{align*} - \frac{1}{2 d x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2243, size = 11, normalized size = 1.1 \begin{align*} -\frac{1}{2 \, d x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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