Optimal. Leaf size=22 \[ \frac {3 (-2+x)}{8-e^3+x+\frac {9 x^2}{25}} \]
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Rubi [A]
time = 0.09, antiderivative size = 28, normalized size of antiderivative = 1.27, number of steps
used = 4, number of rules used = 4, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {1694, 12, 1828,
8} \begin {gather*} -\frac {2700 (2-x)}{324 \left (x+\frac {25}{18}\right )^2+25 \left (263-36 e^3\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 12
Rule 1694
Rule 1828
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\text {Subst}\left (\int \frac {2700 \left (25 \left (263-36 e^3\right )+2196 x-324 x^2\right )}{\left (6575-900 e^3+324 x^2\right )^2} \, dx,x,\frac {25}{18}+x\right )\\ &=2700 \text {Subst}\left (\int \frac {25 \left (263-36 e^3\right )+2196 x-324 x^2}{\left (6575-900 e^3+324 x^2\right )^2} \, dx,x,\frac {25}{18}+x\right )\\ &=-\frac {2700 (2-x)}{25 \left (263-36 e^3\right )+(25+18 x)^2}-\frac {54 \text {Subst}\left (\int 0 \, dx,x,\frac {25}{18}+x\right )}{263-36 e^3}\\ &=-\frac {2700 (2-x)}{25 \left (263-36 e^3\right )+(25+18 x)^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 24, normalized size = 1.09 \begin {gather*} -\frac {75 (2-x)}{200-25 e^3+25 x+9 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 21, normalized size = 0.95
method | result | size |
risch | \(\frac {-3 x +6}{-\frac {9 x^{2}}{25}+{\mathrm e}^{3}-x -8}\) | \(21\) |
gosper | \(-\frac {75 \left (x -2\right )}{-9 x^{2}+25 \,{\mathrm e}^{3}-25 x -200}\) | \(22\) |
norman | \(\frac {-75 x +150}{-9 x^{2}+25 \,{\mathrm e}^{3}-25 x -200}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 21, normalized size = 0.95 \begin {gather*} \frac {75 \, {\left (x - 2\right )}}{9 \, x^{2} + 25 \, x - 25 \, e^{3} + 200} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 21, normalized size = 0.95 \begin {gather*} \frac {75 \, {\left (x - 2\right )}}{9 \, x^{2} + 25 \, x - 25 \, e^{3} + 200} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.24, size = 20, normalized size = 0.91 \begin {gather*} - \frac {150 - 75 x}{9 x^{2} + 25 x - 25 e^{3} + 200} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 21, normalized size = 0.95 \begin {gather*} \frac {75 \, {\left (x - 2\right )}}{9 \, x^{2} + 25 \, x - 25 \, e^{3} + 200} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 22, normalized size = 1.00 \begin {gather*} \frac {75\,x-150}{9\,x^2+25\,x-25\,{\mathrm {e}}^3+200} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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