Optimal. Leaf size=13 \[ -4+x+5 (x+\log (-3 x))^2 \]
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Rubi [A] time = 0.04, antiderivative size = 22, normalized size of antiderivative = 1.69, number of steps used = 5, number of rules used = 4, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.174, Rules used = {14, 2346, 2301, 2295} \begin {gather*} 5 x^2+x+5 \log ^2(-3 x)+10 x \log (-3 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2295
Rule 2301
Rule 2346
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (11+10 x+\frac {10 (1+x) \log (-3 x)}{x}\right ) \, dx\\ &=11 x+5 x^2+10 \int \frac {(1+x) \log (-3 x)}{x} \, dx\\ &=11 x+5 x^2+10 \int \log (-3 x) \, dx+10 \int \frac {\log (-3 x)}{x} \, dx\\ &=x+5 x^2+10 x \log (-3 x)+5 \log ^2(-3 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.69 \begin {gather*} x+5 x^2+10 x \log (-3 x)+5 \log ^2(-3 x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 22, normalized size = 1.69 \begin {gather*} 5 \, x^{2} + 10 \, x \log \left (-3 \, x\right ) + 5 \, \log \left (-3 \, x\right )^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 22, normalized size = 1.69 \begin {gather*} 5 \, x^{2} + 10 \, x \log \left (-3 \, x\right ) + 5 \, \log \left (-3 \, x\right )^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 23, normalized size = 1.77
method | result | size |
derivativedivides | \(10 \ln \left (-3 x \right ) x +x +5 x^{2}+5 \ln \left (-3 x \right )^{2}\) | \(23\) |
default | \(10 \ln \left (-3 x \right ) x +x +5 x^{2}+5 \ln \left (-3 x \right )^{2}\) | \(23\) |
norman | \(10 \ln \left (-3 x \right ) x +x +5 x^{2}+5 \ln \left (-3 x \right )^{2}\) | \(23\) |
risch | \(10 \ln \left (-3 x \right ) x +x +5 x^{2}+5 \ln \left (-3 x \right )^{2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 22, normalized size = 1.69 \begin {gather*} 5 \, x^{2} + 10 \, x \log \left (-3 \, x\right ) + 5 \, \log \left (-3 \, x\right )^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.12, size = 22, normalized size = 1.69 \begin {gather*} 5\,x^2+10\,x\,\ln \left (-3\,x\right )+x+5\,{\ln \left (-3\,x\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 26, normalized size = 2.00 \begin {gather*} 5 x^{2} + 10 x \log {\left (- 3 x \right )} + x + 5 \log {\left (- 3 x \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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