Optimal. Leaf size=25 \[ \frac {\log (5)}{-1+e^x-e^{e^5 (2+x)}+x \log (16)} \]
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Rubi [A]
time = 0.44, antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps
used = 3, number of rules used = 3, integrand size = 94, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {6820, 12, 6818}
\begin {gather*} -\frac {\log (5)}{-e^x+e^{e^5 (x+2)}+x (-\log (16))+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\log (5) \left (-e^x+e^{5+e^5 (2+x)}-\log (16)\right )}{\left (1-e^x+e^{e^5 (2+x)}-x \log (16)\right )^2} \, dx\\ &=\log (5) \int \frac {-e^x+e^{5+e^5 (2+x)}-\log (16)}{\left (1-e^x+e^{e^5 (2+x)}-x \log (16)\right )^2} \, dx\\ &=-\frac {\log (5)}{1-e^x+e^{e^5 (2+x)}-x \log (16)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 25, normalized size = 1.00 \begin {gather*} \frac {\log (5)}{-1+e^x-e^{e^5 (2+x)}+x \log (16)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.65, size = 24, normalized size = 0.96
method | result | size |
norman | \(\frac {\ln \left (5\right )}{{\mathrm e}^{x}-1-{\mathrm e}^{\left (2+x \right ) {\mathrm e}^{5}}+4 x \ln \left (2\right )}\) | \(24\) |
risch | \(\frac {\ln \left (5\right )}{{\mathrm e}^{x}-1-{\mathrm e}^{\left (2+x \right ) {\mathrm e}^{5}}+4 x \ln \left (2\right )}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 26, normalized size = 1.04 \begin {gather*} \frac {\log \left (5\right )}{4 \, x \log \left (2\right ) - e^{\left (x e^{5} + 2 \, e^{5}\right )} + e^{x} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 34, normalized size = 1.36 \begin {gather*} \frac {e^{5} \log \left (5\right )}{4 \, x e^{5} \log \left (2\right ) - e^{5} - e^{\left ({\left (x + 2\right )} e^{5} + 5\right )} + e^{\left (x + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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Giac [A]
time = 0.44, size = 26, normalized size = 1.04 \begin {gather*} \frac {\log \left (5\right )}{4 \, x \log \left (2\right ) - e^{\left (x e^{5} + 2 \, e^{5}\right )} + e^{x} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {4\,\ln \left (2\right )\,\ln \left (5\right )+{\mathrm {e}}^x\,\ln \left (5\right )-{\mathrm {e}}^{{\mathrm {e}}^5\,\left (x+2\right )}\,{\mathrm {e}}^5\,\ln \left (5\right )}{{\mathrm {e}}^{2\,{\mathrm {e}}^5\,\left (x+2\right )}+{\mathrm {e}}^{2\,x}+16\,x^2\,{\ln \left (2\right )}^2-{\mathrm {e}}^{{\mathrm {e}}^5\,\left (x+2\right )}\,\left (2\,{\mathrm {e}}^x+8\,x\,\ln \left (2\right )-2\right )-8\,x\,\ln \left (2\right )+{\mathrm {e}}^x\,\left (8\,x\,\ln \left (2\right )-2\right )+1} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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