Optimal. Leaf size=8 \[ \frac{1}{4} \tan ^{-1}\left (x^4\right ) \]
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Rubi [A] time = 0.0029167, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {275, 203} \[ \frac{1}{4} \tan ^{-1}\left (x^4\right ) \]
Antiderivative was successfully verified.
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Rule 275
Rule 203
Rubi steps
\begin{align*} \int \frac{x^3}{1+x^8} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \frac{1}{1+x^2} \, dx,x,x^4\right )\\ &=\frac{1}{4} \tan ^{-1}\left (x^4\right )\\ \end{align*}
Mathematica [A] time = 0.0034613, size = 8, normalized size = 1. \[ \frac{1}{4} \tan ^{-1}\left (x^4\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 7, normalized size = 0.9 \begin{align*}{\frac{\arctan \left ({x}^{4} \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.45552, size = 8, normalized size = 1. \begin{align*} \frac{1}{4} \, \arctan \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.18346, size = 23, normalized size = 2.88 \begin{align*} \frac{1}{4} \, \arctan \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.101436, size = 5, normalized size = 0.62 \begin{align*} \frac{\operatorname{atan}{\left (x^{4} \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15097, size = 8, normalized size = 1. \begin{align*} \frac{1}{4} \, \arctan \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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