Optimal. Leaf size=19 \[ \frac {81 \left (-x+(4+x)^2\right )^4}{e^8 x^4} \]
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Rubi [B] time = 0.04, antiderivative size = 63, normalized size of antiderivative = 3.32, number of steps used = 3, number of rules used = 2, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {12, 14} \begin {gather*} \frac {81 x^4}{e^8}+\frac {5308416}{e^8 x^4}+\frac {2268 x^3}{e^8}+\frac {9289728}{e^8 x^3}+\frac {28998 x^2}{e^8}+\frac {7423488}{e^8 x^2}+\frac {219996 x}{e^8}+\frac {3519936}{e^8 x} \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 {-21233664-27869184 x-14846976 x^2-3519936 x^3+219996 x^5+57996 x^6+6804 x^7+324 x^8}{x^5} \, dx}{e^8}\\ &=\frac {\int \left (219996-\frac {21233664}{x^5}-\frac {27869184}{x^4}-\frac {14846976}{x^3}-\frac {3519936}{x^2}+57996 x+6804 x^2+324 x^3\right ) \, dx}{e^8}\\ &=\frac {5308416}{e^8 x^4}+\frac {9289728}{e^8 x^3}+\frac {7423488}{e^8 x^2}+\frac {3519936}{e^8 x}+\frac {219996 x}{e^8}+\frac {28998 x^2}{e^8}+\frac {2268 x^3}{e^8}+\frac {81 x^4}{e^8}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 48, normalized size = 2.53 \begin {gather*} \frac {324 \left (\frac {16384}{x^4}+\frac {28672}{x^3}+\frac {22912}{x^2}+\frac {10864}{x}+679 x+\frac {179 x^2}{2}+7 x^3+\frac {x^4}{4}\right )}{e^8} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.13, size = 40, normalized size = 2.11 \begin {gather*} \frac {81 \, {\left (x^{8} + 28 \, x^{7} + 358 \, x^{6} + 2716 \, x^{5} + 43456 \, x^{3} + 91648 \, x^{2} + 114688 \, x + 65536\right )} e^{\left (-8\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.34, size = 41, normalized size = 2.16 \begin {gather*} 81 \, {\left (x^{4} + 28 \, x^{3} + 358 \, x^{2} + 2716 \, x + \frac {64 \, {\left (679 \, x^{3} + 1432 \, x^{2} + 1792 \, x + 1024\right )}}{x^{4}}\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 43, normalized size = 2.26
method | result | size |
gosper | \(\frac {81 \left (x^{8}+28 x^{7}+358 x^{6}+2716 x^{5}+43456 x^{3}+91648 x^{2}+114688 x +65536\right ) {\mathrm e}^{-8}}{x^{4}}\) | \(43\) |
default | \(324 \,{\mathrm e}^{-8} \left (\frac {x^{4}}{4}+7 x^{3}+\frac {179 x^{2}}{2}+679 x +\frac {22912}{x^{2}}+\frac {28672}{x^{3}}+\frac {10864}{x}+\frac {16384}{x^{4}}\right )\) | \(46\) |
risch | \(81 \,{\mathrm e}^{-8} x^{4}+2268 \,{\mathrm e}^{-8} x^{3}+28998 \,{\mathrm e}^{-8} x^{2}+219996 \,{\mathrm e}^{-8} x +\frac {{\mathrm e}^{-8} \left (3519936 x^{3}+7423488 x^{2}+9289728 x +5308416\right )}{x^{4}}\) | \(49\) |
norman | \(\frac {\left (5308416 \,{\mathrm e}^{-1}+9289728 \,{\mathrm e}^{-1} x +7423488 x^{2} {\mathrm e}^{-1}+3519936 \,{\mathrm e}^{-1} x^{3}+219996 \,{\mathrm e}^{-1} x^{5}+28998 \,{\mathrm e}^{-1} x^{6}+2268 \,{\mathrm e}^{-1} x^{7}+81 \,{\mathrm e}^{-1} x^{8}\right ) {\mathrm e}^{-7}}{x^{4}}\) | \(77\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 41, normalized size = 2.16 \begin {gather*} 81 \, {\left (x^{4} + 28 \, x^{3} + 358 \, x^{2} + 2716 \, x + \frac {64 \, {\left (679 \, x^{3} + 1432 \, x^{2} + 1792 \, x + 1024\right )}}{x^{4}}\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 48, normalized size = 2.53 \begin {gather*} 219996\,x\,{\mathrm {e}}^{-8}+28998\,x^2\,{\mathrm {e}}^{-8}+2268\,x^3\,{\mathrm {e}}^{-8}+81\,x^4\,{\mathrm {e}}^{-8}+\frac {{\mathrm {e}}^{-8}\,\left (3519936\,x^3+7423488\,x^2+9289728\,x+5308416\right )}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.10, size = 39, normalized size = 2.05 \begin {gather*} \frac {81 x^{4} + 2268 x^{3} + 28998 x^{2} + 219996 x + \frac {3519936 x^{3} + 7423488 x^{2} + 9289728 x + 5308416}{x^{4}}}{e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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