Optimal. Leaf size=18 \[ \frac{x^5}{5}-\frac{1}{5} \log \left (x^5+1\right ) \]
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Rubi [A] time = 0.0080608, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {266, 43} \[ \frac{x^5}{5}-\frac{1}{5} \log \left (x^5+1\right ) \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^9}{1+x^5} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{x}{1+x} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (1+\frac{1}{-1-x}\right ) \, dx,x,x^5\right )\\ &=\frac{x^5}{5}-\frac{1}{5} \log \left (1+x^5\right )\\ \end{align*}
Mathematica [A] time = 0.0022557, size = 18, normalized size = 1. \[ \frac{x^5}{5}-\frac{1}{5} \log \left (x^5+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 15, normalized size = 0.8 \begin{align*}{\frac{{x}^{5}}{5}}-{\frac{\ln \left ({x}^{5}+1 \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04527, size = 19, normalized size = 1.06 \begin{align*} \frac{1}{5} \, x^{5} - \frac{1}{5} \, \log \left (x^{5} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.58839, size = 38, normalized size = 2.11 \begin{align*} \frac{1}{5} \, x^{5} - \frac{1}{5} \, \log \left (x^{5} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.105383, size = 12, normalized size = 0.67 \begin{align*} \frac{x^{5}}{5} - \frac{\log{\left (x^{5} + 1 \right )}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1438, size = 20, normalized size = 1.11 \begin{align*} \frac{1}{5} \, x^{5} - \frac{1}{5} \, \log \left ({\left | x^{5} + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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