Optimal. Leaf size=10 \[ -\frac {1}{2 d x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\frac {1}{2 d x^2} \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} -\frac {1}{2 d x^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{d x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.81, size = 8, normalized size = 0.80 \begin {gather*} -\frac {1}{2 \, d x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 8, normalized size = 0.80 \begin {gather*} -\frac {1}{2 \, d x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.90 \begin {gather*} -\frac {1}{2 d \,x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 8, normalized size = 0.80 \begin {gather*} -\frac {1}{2 \, d x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 8, normalized size = 0.80 \begin {gather*} -\frac {1}{2\,d\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 8, normalized size = 0.80 \begin {gather*} - \frac {1}{2 d x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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