Optimal. Leaf size=14 \[ \frac{1}{4} \log \left (2 (a+b)+x^4\right ) \]
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Rubi [A] time = 0.0030743, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {260} \[ \frac{1}{4} \log \left (2 (a+b)+x^4\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{x^3}{2 (a+b)+x^4} \, dx &=\frac{1}{4} \log \left (2 (a+b)+x^4\right )\\ \end{align*}
Mathematica [A] time = 0.0038151, size = 15, normalized size = 1.07 \[ \frac{1}{4} \log \left (2 a+2 b+x^4\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 14, normalized size = 1. \begin{align*}{\frac{\ln \left ({x}^{4}+2\,a+2\,b \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07164, size = 18, normalized size = 1.29 \begin{align*} \frac{1}{4} \, \log \left (x^{4} + 2 \, a + 2 \, b\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44376, size = 35, normalized size = 2.5 \begin{align*} \frac{1}{4} \, \log \left (x^{4} + 2 \, a + 2 \, b\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.138295, size = 12, normalized size = 0.86 \begin{align*} \frac{\log{\left (2 a + 2 b + x^{4} \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08766, size = 19, normalized size = 1.36 \begin{align*} \frac{1}{4} \, \log \left ({\left | x^{4} + 2 \, a + 2 \, b \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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