Optimal. Leaf size=24 \[ 2 \left (3+e^2+e^5\right ) \left (1-\frac {\frac {5}{3}+e^2}{x^3}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 2, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {12, 30} \begin {gather*} -\frac {2 \left (5+3 e^2\right ) \left (3+e^2+e^5\right )}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (2 \left (5+3 e^2\right ) \left (3+e^2+e^5\right )\right ) \int \frac {1}{x^4} \, dx\\ &=-\frac {2 \left (5+3 e^2\right ) \left (3+e^2+e^5\right )}{3 x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 29, normalized size = 1.21 \begin {gather*} -\frac {30+28 e^2+6 e^4+10 e^5+6 e^7}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 23, normalized size = 0.96 \begin {gather*} -\frac {2 \, {\left (3 \, e^{7} + 5 \, e^{5} + 3 \, e^{4} + 14 \, e^{2} + 15\right )}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 24, normalized size = 1.00 \begin {gather*} -\frac {2 \, {\left ({\left (3 \, e^{2} + 5\right )} e^{5} + 3 \, e^{4} + 14 \, e^{2} + 15\right )}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 27, normalized size = 1.12
method | result | size |
default | \(-\frac {\left (6 \,{\mathrm e}^{2}+10\right ) {\mathrm e}^{5}+6 \,{\mathrm e}^{4}+28 \,{\mathrm e}^{2}+30}{3 x^{3}}\) | \(27\) |
norman | \(\frac {-2 \,{\mathrm e}^{2} {\mathrm e}^{5}-2 \,{\mathrm e}^{4}-\frac {10 \,{\mathrm e}^{5}}{3}-\frac {28 \,{\mathrm e}^{2}}{3}-10}{x^{3}}\) | \(27\) |
gosper | \(-\frac {2 \left (3 \,{\mathrm e}^{2} {\mathrm e}^{5}+3 \,{\mathrm e}^{4}+5 \,{\mathrm e}^{5}+14 \,{\mathrm e}^{2}+15\right )}{3 x^{3}}\) | \(28\) |
risch | \(-\frac {2 \,{\mathrm e}^{5} {\mathrm e}^{2}}{x^{3}}-\frac {10 \,{\mathrm e}^{5}}{3 x^{3}}-\frac {2 \,{\mathrm e}^{4}}{x^{3}}-\frac {28 \,{\mathrm e}^{2}}{3 x^{3}}-\frac {10}{x^{3}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 24, normalized size = 1.00 \begin {gather*} -\frac {2 \, {\left ({\left (3 \, e^{2} + 5\right )} e^{5} + 3 \, e^{4} + 14 \, e^{2} + 15\right )}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.48, size = 23, normalized size = 0.96 \begin {gather*} -\frac {\frac {28\,{\mathrm {e}}^2}{3}+2\,{\mathrm {e}}^4+\frac {10\,{\mathrm {e}}^5}{3}+2\,{\mathrm {e}}^7+10}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 27, normalized size = 1.12 \begin {gather*} - \frac {30 + 28 e^{2} + 6 e^{4} + 10 e^{5} + 6 e^{7}}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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