Optimal. Leaf size=26 \[ \frac {3+\left (-\frac {4}{x}+2 x\right )^2}{-\frac {5}{e^3}+e^2+x} \]
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Rubi [B] time = 0.14, antiderivative size = 109, normalized size of antiderivative = 4.19, number of steps used = 2, number of rules used = 1, integrand size = 91, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {2074} \begin {gather*} -\frac {16 e^3}{\left (5-e^5\right ) x^2}+4 x-\frac {2500-2000 e^5-325 e^6+600 e^{10}+130 e^{11}+16 e^{12}-80 e^{15}-13 e^{16}+4 e^{20}}{e^3 \left (5-e^5\right )^2 \left (-e^3 x-e^5+5\right )}-\frac {16 e^6}{\left (5-e^5\right )^2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4-\frac {32 e^3}{\left (-5+e^5\right ) x^3}+\frac {16 e^6}{\left (-5+e^5\right )^2 x^2}+\frac {-2500+2000 e^5+325 e^6-600 e^{10}-130 e^{11}-16 e^{12}+80 e^{15}+13 e^{16}-4 e^{20}}{\left (-5+e^5\right )^2 \left (-5+e^5+e^3 x\right )^2}\right ) \, dx\\ &=-\frac {16 e^3}{\left (5-e^5\right ) x^2}-\frac {16 e^6}{\left (5-e^5\right )^2 x}+4 x-\frac {2500-2000 e^5-325 e^6+600 e^{10}+130 e^{11}+16 e^{12}-80 e^{15}-13 e^{16}+4 e^{20}}{e^3 \left (5-e^5\right )^2 \left (5-e^5-e^3 x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.04, size = 73, normalized size = 2.81 \begin {gather*} \frac {100 x^2-40 e^5 x^2+4 e^{10} x^2-20 e^3 x^3+4 e^8 x^3+e^6 \left (16-13 x^2+4 x^4\right )}{e^3 x^2 \left (-5+e^5+e^3 x\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.58, size = 72, normalized size = 2.77 \begin {gather*} \frac {4 \, x^{3} e^{8} - 20 \, x^{3} e^{3} + 4 \, x^{2} e^{10} - 40 \, x^{2} e^{5} + 100 \, x^{2} + {\left (4 \, x^{4} - 13 \, x^{2} + 16\right )} e^{6}}{x^{3} e^{6} + x^{2} e^{8} - 5 \, x^{2} e^{3}} \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 = 9.06, size = 32, normalized size = 1.23
method | result | size |
gosper | \(\frac {\left (4 x^{4}-13 x^{2}+16\right ) {\mathrm e}^{3}}{x^{2} \left ({\mathrm e}^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}-5\right )}\) | \(32\) |
norman | \(\frac {-13 x^{2} {\mathrm e}^{3}+4 x^{4} {\mathrm e}^{3}+16 \,{\mathrm e}^{3}}{x^{2} \left ({\mathrm e}^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}-5\right )}\) | \(37\) |
risch | \(4 x +\frac {\left (4 \,{\mathrm e}^{10}-13 \,{\mathrm e}^{6}-40 \,{\mathrm e}^{5}+100\right ) {\mathrm e}^{-3} x^{2}+16 \,{\mathrm e}^{3}}{x^{2} \left ({\mathrm e}^{5}+x \,{\mathrm e}^{3}-5\right )}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 48, normalized size = 1.85 \begin {gather*} 4 \, x + \frac {x^{2} {\left (4 \, e^{10} - 13 \, e^{6} - 40 \, e^{5} + 100\right )} + 16 \, e^{6}}{x^{3} e^{6} + x^{2} {\left (e^{8} - 5 \, e^{3}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.22, size = 48, normalized size = 1.85 \begin {gather*} 4\,x+\frac {16\,{\mathrm {e}}^3-x^2\,{\mathrm {e}}^{-3}\,\left (40\,{\mathrm {e}}^5+13\,{\mathrm {e}}^6-4\,{\mathrm {e}}^{10}-100\right )}{{\mathrm {e}}^3\,x^3+\left ({\mathrm {e}}^5-5\right )\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 5.84, size = 46, normalized size = 1.77 \begin {gather*} 4 x + \frac {x^{2} \left (- 40 e^{5} - 13 e^{6} + 100 + 4 e^{10}\right ) + 16 e^{6}}{x^{3} e^{6} + x^{2} \left (- 5 e^{3} + e^{8}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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