Optimal. Leaf size=20 \[ \log \left (e^{-24 x^2} x \left (e+e^{2 (5+x)}+x\right )\right ) \]
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Rubi [F]
time = 0.35, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {2 x-48 x^3+e \left (1-48 x^2\right )+e^{10+2 x} \left (1+2 x-48 x^2\right )}{e x+e^{10+2 x} x+x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {-1+2 e+2 x}{e+e^{10+2 x}+x}+\frac {1+2 x-48 x^2}{x}\right ) \, dx\\ &=-\int \frac {-1+2 e+2 x}{e+e^{10+2 x}+x} \, dx+\int \frac {1+2 x-48 x^2}{x} \, dx\\ &=\int \left (2+\frac {1}{x}-48 x\right ) \, dx-\int \left (-\frac {1-2 e}{e+e^{10+2 x}+x}+\frac {2 x}{e+e^{10+2 x}+x}\right ) \, dx\\ &=2 x-24 x^2+\log (x)-2 \int \frac {x}{e+e^{10+2 x}+x} \, dx-(-1+2 e) \int \frac {1}{e+e^{10+2 x}+x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.83, size = 19, normalized size = 0.95 \begin {gather*} -24 x^2+\log (x)+\log \left (e+e^{10+2 x}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.40, size = 20, normalized size = 1.00
method | result | size |
norman | \(-24 x^{2}+\ln \left (x \right )+\ln \left ({\mathrm e}^{2 x +10}+x +{\mathrm e}\right )\) | \(20\) |
risch | \(-24 x^{2}+\ln \left (x \right )-10+\ln \left ({\mathrm e}^{2 x +10}+x +{\mathrm e}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 22, normalized size = 1.10 \begin {gather*} -24 \, x^{2} + \log \left ({\left (x + e + e^{\left (2 \, x + 10\right )}\right )} e^{\left (-10\right )}\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 19, normalized size = 0.95 \begin {gather*} -24 \, x^{2} + \log \left (x + e + e^{\left (2 \, x + 10\right )}\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 20, normalized size = 1.00 \begin {gather*} - 24 x^{2} + \log {\left (x \right )} + \log {\left (x + e^{2 x + 10} + e \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 25, normalized size = 1.25 \begin {gather*} -24 \, x^{2} + \log \left (x\right ) + \log \left (-x - e - e^{\left (2 \, x + 10\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.16, size = 19, normalized size = 0.95 \begin {gather*} \ln \left (x+\mathrm {e}+{\mathrm {e}}^{2\,x+10}\right )+\ln \left (x\right )-24\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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