Optimal. Leaf size=16 \[ -6-\frac {256}{x^4}+2 x+\log \left (3+e^x\right ) \]
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Rubi [A]
time = 0.11, antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps
used = 8, number of rules used = 6, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {6874, 2320, 36,
29, 31, 14} \begin {gather*} -\frac {256}{x^4}+2 x+\log \left (e^x+3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 29
Rule 31
Rule 36
Rule 2320
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {3}{3+e^x}+\frac {1024+3 x^5}{x^5}\right ) \, dx\\ &=-\left (3 \int \frac {1}{3+e^x} \, dx\right )+\int \frac {1024+3 x^5}{x^5} \, dx\\ &=-\left (3 \text {Subst}\left (\int \frac {1}{x (3+x)} \, dx,x,e^x\right )\right )+\int \left (3+\frac {1024}{x^5}\right ) \, dx\\ &=-\frac {256}{x^4}+3 x-\text {Subst}\left (\int \frac {1}{x} \, dx,x,e^x\right )+\text {Subst}\left (\int \frac {1}{3+x} \, dx,x,e^x\right )\\ &=-\frac {256}{x^4}+2 x+\log \left (3+e^x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 1.13, size = 21, normalized size = 1.31 \begin {gather*} -\frac {256}{x^4}+3 x-\log \left (e^x\right )+\log \left (3+e^x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.17, size = 15, normalized size = 0.94
method | result | size |
risch | \(2 x -\frac {256}{x^{4}}+\ln \left (3+{\mathrm e}^{x}\right )\) | \(15\) |
norman | \(\frac {2 x^{5}-256}{x^{4}}+\ln \left (3+{\mathrm e}^{x}\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 16, normalized size = 1.00 \begin {gather*} \frac {2 \, {\left (x^{5} - 128\right )}}{x^{4}} + \log \left (e^{x} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.47, size = 20, normalized size = 1.25 \begin {gather*} \frac {2 \, x^{5} + x^{4} \log \left (e^{x} + 3\right ) - 256}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 14, normalized size = 0.88 \begin {gather*} 2 x + \log {\left (e^{x} + 3 \right )} - \frac {256}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 20, normalized size = 1.25 \begin {gather*} \frac {2 \, x^{5} + x^{4} \log \left (e^{x} + 3\right ) - 256}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.74, size = 17, normalized size = 1.06 \begin {gather*} \ln \left ({\mathrm {e}}^x+3\right )+\frac {2\,x^5-256}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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