Optimal. Leaf size=22 \[ \frac {3 \left (5-\frac {900000000}{e^{16} x^4}\right ) \left (-\frac {2}{x}+x\right )}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {12, 14} \begin {gather*} \frac {5400000000}{e^{16} x^6}-\frac {2700000000}{e^{16} x^4}-\frac {30}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-32400000000+10800000000 x^2+60 e^{16} x^4}{x^7} \, dx}{e^{16}}\\ &=\frac {\int \left (-\frac {32400000000}{x^7}+\frac {10800000000}{x^5}+\frac {60 e^{16}}{x^3}\right ) \, dx}{e^{16}}\\ &=\frac {5400000000}{e^{16} x^6}-\frac {2700000000}{e^{16} x^4}-\frac {30}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 26, normalized size = 1.18 \begin {gather*} \frac {60 \left (\frac {90000000}{x^6}-\frac {45000000}{x^4}-\frac {e^{16}}{2 x^2}\right )}{e^{16}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 20, normalized size = 0.91 \begin {gather*} -\frac {30 \, {\left (x^{4} e^{16} + 90000000 \, x^{2} - 180000000\right )} e^{\left (-16\right )}}{x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 20, normalized size = 0.91 \begin {gather*} -\frac {30 \, {\left (x^{4} e^{16} + 90000000 \, x^{2} - 180000000\right )} e^{\left (-16\right )}}{x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.95
method | result | size |
risch | \(\frac {{\mathrm e}^{-16} \left (-30 x^{4} {\mathrm e}^{16}-2700000000 x^{2}+5400000000\right )}{x^{6}}\) | \(21\) |
gosper | \(-\frac {30 \left (x^{4} {\mathrm e}^{16}+90000000 x^{2}-180000000\right ) {\mathrm e}^{-16}}{x^{6}}\) | \(25\) |
default | \(60 \,{\mathrm e}^{-16} \left (-\frac {{\mathrm e}^{16}}{2 x^{2}}-\frac {45000000}{x^{4}}+\frac {90000000}{x^{6}}\right )\) | \(25\) |
norman | \(\frac {\left (5400000000 \,{\mathrm e}^{-4}-2700000000 x^{2} {\mathrm e}^{-4}-30 x^{4} {\mathrm e}^{12}\right ) {\mathrm e}^{-12}}{x^{6}}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 20, normalized size = 0.91 \begin {gather*} -\frac {30 \, {\left (x^{4} e^{16} + 90000000 \, x^{2} - 180000000\right )} e^{\left (-16\right )}}{x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 21, normalized size = 0.95 \begin {gather*} -\frac {{\mathrm {e}}^{-16}\,\left (30\,{\mathrm {e}}^{16}\,x^4+2700000000\,x^2-5400000000\right )}{x^6} \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 {- 30 x^{4} e^{16} - 2700000000 x^{2} + 5400000000}{x^{6} e^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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