Optimal. Leaf size=10 \[ \frac {3}{(-16+x) x^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.20, number of steps
used = 3, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {1608, 27, 75}
\begin {gather*} -\frac {3}{(16-x) x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 75
Rule 1608
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {96-9 x}{x^3 \left (256-32 x+x^2\right )} \, dx\\ &=\int \frac {96-9 x}{(-16+x)^2 x^3} \, dx\\ &=-\frac {3}{(16-x) x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {3}{(-16+x) x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 19, normalized size = 1.90
method | result | size |
gosper | \(\frac {3}{x^{2} \left (x -16\right )}\) | \(11\) |
norman | \(\frac {3}{x^{2} \left (x -16\right )}\) | \(11\) |
risch | \(\frac {3}{x^{2} \left (x -16\right )}\) | \(11\) |
default | \(\frac {3}{256 \left (x -16\right )}-\frac {3}{16 x^{2}}-\frac {3}{256 x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 1.30 \begin {gather*} \frac {3}{x^{3} - 16 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 13, normalized size = 1.30 \begin {gather*} \frac {3}{x^{3} - 16 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 8, normalized size = 0.80 \begin {gather*} \frac {3}{x^{3} - 16 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 16, normalized size = 1.60 \begin {gather*} \frac {3}{256 \, {\left (x - 16\right )}} - \frac {3 \, {\left (x + 16\right )}}{256 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.22, size = 15, normalized size = 1.50 \begin {gather*} -\frac {3}{16\,x^2-x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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