Optimal. Leaf size=20 \[ e^3-e^{2 e^x}+e^x+\frac {1}{\log ^4(x)} \]
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Rubi [A]
time = 0.15, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps
used = 7, number of rules used = 5, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {6820, 2225,
2320, 2339, 30} \begin {gather*} -e^{2 e^x}+e^x+\frac {1}{\log ^4(x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rule 2225
Rule 2320
Rule 2339
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x-2 e^{2 e^x+x}-\frac {4}{x \log ^5(x)}\right ) \, dx\\ &=-\left (2 \int e^{2 e^x+x} \, dx\right )-4 \int \frac {1}{x \log ^5(x)} \, dx+\int e^x \, dx\\ &=e^x-2 \text {Subst}\left (\int e^{2 x} \, dx,x,e^x\right )-4 \text {Subst}\left (\int \frac {1}{x^5} \, dx,x,\log (x)\right )\\ &=-e^{2 e^x}+e^x+\frac {1}{\log ^4(x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 17, normalized size = 0.85 \begin {gather*} -e^{2 e^x}+e^x+\frac {1}{\log ^4(x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 15, normalized size = 0.75
method | result | size |
default | \({\mathrm e}^{x}-{\mathrm e}^{2 \,{\mathrm e}^{x}}+\frac {1}{\ln \left (x \right )^{4}}\) | \(15\) |
risch | \({\mathrm e}^{x}-{\mathrm e}^{2 \,{\mathrm e}^{x}}+\frac {1}{\ln \left (x \right )^{4}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 14, normalized size = 0.70 \begin {gather*} \frac {1}{\log \left (x\right )^{4}} + e^{x} - e^{\left (2 \, e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 34 vs.
\(2 (16) = 32\).
time = 0.37, size = 34, normalized size = 1.70 \begin {gather*} \frac {{\left (e^{\left (2 \, x\right )} \log \left (x\right )^{4} - e^{\left (x + 2 \, e^{x}\right )} \log \left (x\right )^{4} + e^{x}\right )} e^{\left (-x\right )}}{\log \left (x\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 15, normalized size = 0.75 \begin {gather*} e^{x} - e^{2 e^{x}} + \frac {1}{\log {\left (x \right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 34 vs.
\(2 (16) = 32\).
time = 0.43, size = 34, normalized size = 1.70 \begin {gather*} \frac {{\left (e^{\left (2 \, x\right )} \log \left (x\right )^{4} - e^{\left (x + 2 \, e^{x}\right )} \log \left (x\right )^{4} + e^{x}\right )} e^{\left (-x\right )}}{\log \left (x\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.19, size = 14, normalized size = 0.70 \begin {gather*} {\mathrm {e}}^x-{\mathrm {e}}^{2\,{\mathrm {e}}^x}+\frac {1}{{\ln \left (x\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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