Optimal. Leaf size=16 \[ x \log \left (x^3+x\right )-3 x+2 \tan ^{-1}(x) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2523, 388, 203} \[ x \log \left (x^3+x\right )-3 x+2 \tan ^{-1}(x) \]
Antiderivative was successfully verified.
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Rule 203
Rule 388
Rule 2523
Rubi steps
\begin {align*} \int \log \left (x+x^3\right ) \, dx &=x \log \left (x+x^3\right )-\int \frac {1+3 x^2}{1+x^2} \, dx\\ &=-3 x+x \log \left (x+x^3\right )+2 \int \frac {1}{1+x^2} \, dx\\ &=-3 x+2 \tan ^{-1}(x)+x \log \left (x+x^3\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ x \log \left (x^3+x\right )-3 x+2 \tan ^{-1}(x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 16, normalized size = 1.00 \[ x \log \left (x^{3} + x\right ) - 3 \, x + 2 \, \arctan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 16, normalized size = 1.00 \[ x \log \left (x^{3} + x\right ) - 3 \, x + 2 \, \arctan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 17, normalized size = 1.06 \[ x \ln \left (x^{3}+x \right )-3 x +2 \arctan \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.55, size = 16, normalized size = 1.00 \[ x \log \left (x^{3} + x\right ) - 3 \, x + 2 \, \arctan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 16, normalized size = 1.00 \[ 2\,\mathrm {atan}\relax (x)-3\,x+x\,\ln \left (x^3+x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 15, normalized size = 0.94 \[ x \log {\left (x^{3} + x \right )} - 3 x + 2 \operatorname {atan}{\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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