Optimal. Leaf size=35 \[ \frac {2}{15}+\frac {x}{5-\frac {x}{3}}+\frac {4}{x \left (-e^4+\frac {2}{2+x}\right )} \]
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Rubi [A] time = 0.21, antiderivative size = 53, normalized size of antiderivative = 1.51, number of steps used = 2, number of rules used = 1, integrand size = 126, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2074} \begin {gather*} \frac {4}{\left (1-e^4\right ) x}+\frac {4}{\left (1-e^4\right ) \left (2 \left (1-e^4\right )-e^4 x\right )}+\frac {45}{15-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {45}{(-15+x)^2}+\frac {4}{\left (-1+e^4\right ) x^2}-\frac {4 e^4}{\left (-1+e^4\right ) \left (-2+2 e^4+e^4 x\right )^2}\right ) \, dx\\ &=\frac {45}{15-x}+\frac {4}{\left (1-e^4\right ) x}+\frac {4}{\left (1-e^4\right ) \left (2 \left (1-e^4\right )-e^4 x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 46, normalized size = 1.31 \begin {gather*} \frac {120+\left (142-90 e^4\right ) x-\left (4+45 e^4\right ) x^2}{x \left (30-2 x+e^4 \left (-30-13 x+x^2\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 49, normalized size = 1.40 \begin {gather*} \frac {4 \, x^{2} + 45 \, {\left (x^{2} + 2 \, x\right )} e^{4} - 142 \, x - 120}{2 \, x^{2} - {\left (x^{3} - 13 \, x^{2} - 30 \, x\right )} e^{4} - 30 \, x} \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 = 55.98, size = 47, normalized size = 1.34
method | result | size |
risch | \(\frac {\left (-45 \,{\mathrm e}^{4}-4\right ) x^{2}+\left (-90 \,{\mathrm e}^{4}+142\right ) x +120}{\left (x^{2} {\mathrm e}^{4}-13 x \,{\mathrm e}^{4}-30 \,{\mathrm e}^{4}-2 x +30\right ) x}\) | \(47\) |
gosper | \(-\frac {45 x^{2} {\mathrm e}^{4}+90 x \,{\mathrm e}^{4}+4 x^{2}-142 x -120}{x \left (x^{2} {\mathrm e}^{4}-13 x \,{\mathrm e}^{4}-30 \,{\mathrm e}^{4}-2 x +30\right )}\) | \(50\) |
norman | \(\frac {120-\left (45 \,{\mathrm e}^{8}+4 \,{\mathrm e}^{4}\right ) {\mathrm e}^{-4} x^{2}-2 \left (45 \,{\mathrm e}^{8}-71 \,{\mathrm e}^{4}\right ) {\mathrm e}^{-4} x}{x \left (x -15\right ) \left (x \,{\mathrm e}^{4}+2 \,{\mathrm e}^{4}-2\right )}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 50, normalized size = 1.43 \begin {gather*} -\frac {x^{2} {\left (45 \, e^{4} + 4\right )} + 2 \, x {\left (45 \, e^{4} - 71\right )} - 120}{x^{3} e^{4} - x^{2} {\left (13 \, e^{4} + 2\right )} - 30 \, x {\left (e^{4} - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.35, size = 39, normalized size = 1.11 \begin {gather*} \frac {4}{\left ({\mathrm {e}}^4-1\right )\,\left (2\,{\mathrm {e}}^4+x\,{\mathrm {e}}^4-2\right )}-\frac {45}{x-15}-\frac {4}{x\,\left ({\mathrm {e}}^4-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.84, size = 48, normalized size = 1.37 \begin {gather*} \frac {x^{2} \left (- 45 e^{4} - 4\right ) + x \left (142 - 90 e^{4}\right ) + 120}{x^{3} e^{4} + x^{2} \left (- 13 e^{4} - 2\right ) + x \left (30 - 30 e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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