Optimal. Leaf size=16 \[ 1-25 x \left (-e^{2 x}+x\right )+\log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.94, number of steps used = 6, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {14, 2176, 2194} \begin {gather*} -25 x^2-\frac {25 e^{2 x}}{2}+\frac {25}{2} e^{2 x} (2 x+1)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (25 e^{2 x} (1+2 x)+\frac {1-50 x^2}{x}\right ) \, dx\\ &=25 \int e^{2 x} (1+2 x) \, dx+\int \frac {1-50 x^2}{x} \, dx\\ &=\frac {25}{2} e^{2 x} (1+2 x)-25 \int e^{2 x} \, dx+\int \left (\frac {1}{x}-50 x\right ) \, dx\\ &=-\frac {25 e^{2 x}}{2}-25 x^2+\frac {25}{2} e^{2 x} (1+2 x)+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} 25 e^{2 x} x-25 x^2+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 15, normalized size = 0.94 \begin {gather*} -25 \, x^{2} + 25 \, x e^{\left (2 \, x\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.94 \begin {gather*} -25 \, x^{2} + 25 \, x e^{\left (2 \, x\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 16, normalized size = 1.00
method | result | size |
norman | \(-25 x^{2}+25 x \,{\mathrm e}^{2 x}+\ln \relax (x )\) | \(16\) |
risch | \(-25 x^{2}+25 x \,{\mathrm e}^{2 x}+\ln \relax (x )\) | \(16\) |
derivativedivides | \(-25 x^{2}+\ln \left (2 x \right )+25 x \,{\mathrm e}^{2 x}\) | \(18\) |
default | \(-25 x^{2}+\ln \left (2 x \right )+25 x \,{\mathrm e}^{2 x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 25, normalized size = 1.56 \begin {gather*} -25 \, x^{2} + \frac {25}{2} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + \frac {25}{2} \, e^{\left (2 \, x\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.24, size = 15, normalized size = 0.94 \begin {gather*} \ln \relax (x)+25\,x\,{\mathrm {e}}^{2\,x}-25\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 15, normalized size = 0.94 \begin {gather*} - 25 x^{2} + 25 x e^{2 x} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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