Optimal. Leaf size=19 \[ \frac {3 x}{e (4-x+4 (-36+x) x)} \]
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Rubi [A] time = 0.06, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 4, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.121, Rules used = {12, 1680, 1814, 8} \begin {gather*} -\frac {48 x}{e \left (20961-(145-8 x)^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 12
Rule 1680
Rule 1814
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {12-12 x^2}{16-1160 x+21057 x^2-1160 x^3+16 x^4} \, dx}{e}\\ &=\frac {\operatorname {Subst}\left (\int \frac {48 \left (-20961-2320 x-64 x^2\right )}{\left (20961-64 x^2\right )^2} \, dx,x,-\frac {145}{8}+x\right )}{e}\\ &=\frac {48 \operatorname {Subst}\left (\int \frac {-20961-2320 x-64 x^2}{\left (20961-64 x^2\right )^2} \, dx,x,-\frac {145}{8}+x\right )}{e}\\ &=-\frac {48 x}{e \left (20961-(145-8 x)^2\right )}-\frac {8 \operatorname {Subst}\left (\int 0 \, dx,x,-\frac {145}{8}+x\right )}{6987 e}\\ &=-\frac {48 x}{e \left (20961-(145-8 x)^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.95 \begin {gather*} \frac {3 x}{e \left (4-145 x+4 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 17, normalized size = 0.89 \begin {gather*} \frac {3 \, x e^{\left (-1\right )}}{4 \, x^{2} - 145 \, x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 16, normalized size = 0.84 \begin {gather*} \frac {3 \, e^{\left (-1\right )}}{4 \, x + \frac {4}{x} - 145} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 0.84
method | result | size |
risch | \(\frac {3 \,{\mathrm e}^{-1} x}{4 \left (x^{2}-\frac {145}{4} x +1\right )}\) | \(16\) |
default | \(\frac {3 \,{\mathrm e}^{-1} x}{4 \left (x^{2}-\frac {145}{4} x +1\right )}\) | \(18\) |
gosper | \(\frac {3 x \,{\mathrm e}^{-1}}{4 x^{2}-145 x +4}\) | \(20\) |
norman | \(\frac {3 x \,{\mathrm e}^{-1}}{4 x^{2}-145 x +4}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 17, normalized size = 0.89 \begin {gather*} \frac {3 \, x e^{\left (-1\right )}}{4 \, x^{2} - 145 \, x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 17, normalized size = 0.89 \begin {gather*} \frac {3\,x\,{\mathrm {e}}^{-1}}{4\,x^2-145\,x+4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 22, normalized size = 1.16 \begin {gather*} \frac {3 x}{4 e x^{2} - 145 e x + 4 e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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