Optimal. Leaf size=19 \[ \log \left (\frac {x}{e^{(3+5 (-4+\log (x)))^2}+x}\right ) \]
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Rubi [F] time = 1.06, 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 {e^{289+25 \log ^2(x)} (171-50 \log (x))}{x^{170} \left (\frac {e^{289+25 \log ^2(x)}}{x^{169}}+x^2\right )} \, 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 {171 e^{289+25 \log ^2(x)}}{e^{289+25 \log ^2(x)} x+x^{172}}-\frac {50 e^{289+25 \log ^2(x)} \log (x)}{e^{289+25 \log ^2(x)} x+x^{172}}\right ) \, dx\\ &=-\left (50 \int \frac {e^{289+25 \log ^2(x)} \log (x)}{e^{289+25 \log ^2(x)} x+x^{172}} \, dx\right )+171 \int \frac {e^{289+25 \log ^2(x)}}{e^{289+25 \log ^2(x)} x+x^{172}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 22, normalized size = 1.16 \begin {gather*} 171 \log (x)-\log \left (e^{289+25 \log ^2(x)}+x^{171}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 21, normalized size = 1.11 \begin {gather*} -\log \left (x + e^{\left (25 \, \log \relax (x)^{2} - 170 \, \log \relax (x) + 289\right )}\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 21, normalized size = 1.11 \begin {gather*} -\log \left (x^{171} + e^{\left (25 \, \log \relax (x)^{2} + 289\right )}\right ) + 171 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 22, normalized size = 1.16
method | result | size |
norman | \(\ln \relax (x )-\ln \left ({\mathrm e}^{25 \ln \relax (x )^{2}-170 \ln \relax (x )+289}+x \right )\) | \(22\) |
risch | \(\ln \relax (x )+289-\ln \left (\frac {{\mathrm e}^{25 \ln \relax (x )^{2}+289}}{x^{170}}+x \right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-1)] 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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mupad [B] time = 4.45, size = 22, normalized size = 1.16 \begin {gather*} \ln \left (x^{171}\right )-\ln \left ({\mathrm {e}}^{25\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{289}+x^{171}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 19, normalized size = 1.00 \begin {gather*} 171 \log {\relax (x )} - \log {\left (x^{171} + e^{25 \log {\relax (x )}^{2} + 289} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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