Optimal. Leaf size=7 \[ -\frac {1}{3 x^3} \]
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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {30}
\begin {gather*} -\frac {1}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rubi steps
\begin {align*} \int \frac {1}{x^4} \, dx &=-\frac {1}{3 x^3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} -\frac {1}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 6, normalized size = 0.86
method | result | size |
gosper | \(-\frac {1}{3 x^{3}}\) | \(6\) |
default | \(-\frac {1}{3 x^{3}}\) | \(6\) |
norman | \(-\frac {1}{3 x^{3}}\) | \(6\) |
risch | \(-\frac {1}{3 x^{3}}\) | \(6\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.69, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 1.00 \begin {gather*} - \frac {1}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.28, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.01, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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