Optimal. Leaf size=11 \[ \frac {1}{3 (3-x)^3} \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {32}
\begin {gather*} \frac {1}{3 (3-x)^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{(-3+x)^4} \, dx &=\frac {1}{3 (3-x)^3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} -\frac {1}{3 (-3+x)^3} \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.77, size = 19, normalized size = 1.73 \begin {gather*} -\frac {1}{-81+81 x-27 x^2+3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 8, normalized size = 0.73
method | result | size |
gosper | \(-\frac {1}{3 \left (-3+x \right )^{3}}\) | \(8\) |
default | \(-\frac {1}{3 \left (-3+x \right )^{3}}\) | \(8\) |
norman | \(-\frac {1}{3 \left (-3+x \right )^{3}}\) | \(8\) |
risch | \(-\frac {1}{3 \left (-3+x \right )^{3}}\) | \(8\) |
meijerg | \(\frac {x \left (\frac {1}{9} x^{2}-x +3\right )}{243 \left (1-\frac {x}{3}\right )^{3}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 7, normalized size = 0.64 \begin {gather*} -\frac {1}{3 \, {\left (x - 3\right )}^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 17 vs.
\(2 (7) = 14\).
time = 0.31, size = 17, normalized size = 1.55 \begin {gather*} -\frac {1}{3 \, {\left (x^{3} - 9 \, x^{2} + 27 \, x - 27\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 17 vs.
\(2 (7) = 14\)
time = 0.05, size = 17, normalized size = 1.55 \begin {gather*} - \frac {1}{3 x^{3} - 27 x^{2} + 81 x - 81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} -\frac 1{3 \left (x-3\right )^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 7, normalized size = 0.64 \begin {gather*} -\frac {1}{3\,{\left (x-3\right )}^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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