Optimal. Leaf size=9 \[ e^{9 e^{10 x}} \]
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Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2282, 2194} \begin {gather*} e^{9 e^{10 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=90 \int e^{9 e^{10 x}+10 x} \, dx\\ &=9 \operatorname {Subst}\left (\int e^{9 x} \, dx,x,e^{10 x}\right )\\ &=e^{9 e^{10 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 1.00 \begin {gather*} e^{9 e^{10 x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 7, normalized size = 0.78 \begin {gather*} e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 7, normalized size = 0.78 \begin {gather*} e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 8, normalized size = 0.89
method | result | size |
derivativedivides | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
default | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
norman | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
risch | \({\mathrm e}^{9 \,{\mathrm e}^{10 x}}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 7, normalized size = 0.78 \begin {gather*} e^{\left (9 \, e^{\left (10 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 7, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{9\,{\mathrm {e}}^{10\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 7, normalized size = 0.78 \begin {gather*} e^{9 e^{10 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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