Optimal. Leaf size=28 \[ \frac {e^2}{3+e^{5 \left (e^{e^{e^{10 x}}}+x\right ) \left (e^x+x\right )}} \]
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Rubi [A] time = 14.39, antiderivative size = 33, normalized size of antiderivative = 1.18, number of steps used = 3, number of rules used = 3, integrand size = 174, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6741, 6711, 32} \begin {gather*} -\frac {e^2}{3 \left (3 e^{-5 \left (x+e^{e^{e^{10 x}}}\right ) \left (x+e^x\right )}+1\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rule 6711
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{5 \left (e^{e^{e^{10 x}}}+x\right ) \left (e^x+x\right )} \left (e^{2+x} (-5-5 x)-10 e^2 x+e^{e^{e^{10 x}}} \left (-5 e^2-5 e^{2+x}+e^{e^{10 x}+10 x} \left (-50 e^{2+x}-50 e^2 x\right )\right )\right )}{\left (3+e^{5 \left (e^{e^{e^{10 x}}}+x\right ) \left (e^x+x\right )}\right )^2} \, dx\\ &=\frac {1}{3} e^2 \operatorname {Subst}\left (\int \frac {1}{(1+x)^2} \, dx,x,3 e^{-5 \left (e^{e^{e^{10 x}}}+x\right ) \left (e^x+x\right )}\right )\\ &=-\frac {e^2}{3 \left (1+3 e^{-5 \left (e^{e^{e^{10 x}}}+x\right ) \left (e^x+x\right )}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.30, size = 28, normalized size = 1.00 \begin {gather*} \frac {e^2}{3+e^{5 \left (e^{e^{e^{10 x}}}+x\right ) \left (e^x+x\right )}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.70, size = 56, normalized size = 2.00 \begin {gather*} \frac {e^{2}}{e^{\left (5 \, {\left (x^{2} e^{2} + x e^{\left (x + 2\right )} + {\left (x e^{2} + e^{\left (x + 2\right )}\right )} e^{\left (e^{\left ({\left (10 \, x e^{20} + e^{\left (10 \, x + 20\right )}\right )} e^{\left (-20\right )} - 10 \, x\right )}\right )}\right )} e^{\left (-2\right )}\right )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 23, normalized size = 0.82
method | result | size |
risch | \(\frac {{\mathrm e}^{2}}{{\mathrm e}^{5 \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{10 x}}}+x \right ) \left ({\mathrm e}^{x}+x \right )}+3}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.97, size = 38, normalized size = 1.36 \begin {gather*} \frac {e^{2}}{e^{\left (5 \, x^{2} + 5 \, x e^{x} + 5 \, x e^{\left (e^{\left (e^{\left (10 \, x\right )}\right )}\right )} + 5 \, e^{\left (x + e^{\left (e^{\left (10 \, x\right )}\right )}\right )}\right )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.76, size = 41, normalized size = 1.46 \begin {gather*} \frac {{\mathrm {e}}^2}{{\mathrm {e}}^{5\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{5\,x\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{10\,x}}}}\,{\mathrm {e}}^{5\,x^2}\,{\mathrm {e}}^{5\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{10\,x}}}\,{\mathrm {e}}^x}+3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.81, size = 34, normalized size = 1.21 \begin {gather*} \frac {e^{2}}{e^{5 x^{2} + 5 x e^{x} + \left (5 x + 5 e^{x}\right ) e^{e^{e^{10 x}}}} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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