Optimal. Leaf size=19 \[ e^2 \left (10+\frac {84}{5 (4 (9+e)+x)}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.84, number of steps used = 5, number of rules used = 4, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.138, Rules used = {12, 1981, 27, 32} \begin {gather*} \frac {84 e^2}{5 (x+4 (9+e))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rule 1981
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (84 e^2\right ) \int \frac {1}{6480+80 e^2+360 x+5 x^2+e (1440+40 x)} \, dx\right )\\ &=-\left (\left (84 e^2\right ) \int \frac {1}{80 (9+e)^2+40 (9+e) x+5 x^2} \, dx\right )\\ &=-\left (\left (84 e^2\right ) \int \frac {1}{5 (36+4 e+x)^2} \, dx\right )\\ &=-\left (\frac {1}{5} \left (84 e^2\right ) \int \frac {1}{(36+4 e+x)^2} \, dx\right )\\ &=\frac {84 e^2}{5 (4 (9+e)+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.79 \begin {gather*} \frac {84 e^2}{5 (36+4 e+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 13, normalized size = 0.68 \begin {gather*} \frac {84 \, e^{2}}{5 \, {\left (x + 4 \, e + 36\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 14, normalized size = 0.74
method | result | size |
gosper | \(\frac {84 \,{\mathrm e}^{2}}{5 \left (4 \,{\mathrm e}+x +36\right )}\) | \(14\) |
norman | \(\frac {84 \,{\mathrm e}^{2}}{5 \left (4 \,{\mathrm e}+x +36\right )}\) | \(14\) |
risch | \(\frac {21 \,{\mathrm e}^{2}}{5 \left ({\mathrm e}+\frac {x}{4}+9\right )}\) | \(14\) |
meijerg | \(-\frac {21 \,{\mathrm e}^{2} x}{5 \left (4 \,{\mathrm e}+36\right ) \left ({\mathrm e}+9\right ) \left (1+\frac {x}{4 \,{\mathrm e}+36}\right )}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 13, normalized size = 0.68 \begin {gather*} \frac {84 \, e^{2}}{5 \, {\left (x + 4 \, e + 36\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.35, size = 15, normalized size = 0.79 \begin {gather*} \frac {84\,{\mathrm {e}}^2}{5\,\left (x+4\,\mathrm {e}+36\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 14, normalized size = 0.74 \begin {gather*} \frac {84 e^{2}}{5 x + 20 e + 180} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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