Optimal. Leaf size=24 \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]
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Rubi [A] time = 0.0138791, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^9}{2 b+b x^5} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{x}{2 b+b x} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (\frac{1}{b}-\frac{2}{b (2+x)}\right ) \, dx,x,x^5\right )\\ &=\frac{x^5}{5 b}-\frac{2 \log \left (2+x^5\right )}{5 b}\\ \end{align*}
Mathematica [A] time = 0.0032358, size = 24, normalized size = 1. \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 21, normalized size = 0.9 \begin{align*}{\frac{{x}^{5}}{5\,b}}-{\frac{2\,\ln \left ({x}^{5}+2 \right ) }{5\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02867, size = 27, normalized size = 1.12 \begin{align*} \frac{x^{5}}{5 \, b} - \frac{2 \, \log \left (x^{5} + 2\right )}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.92924, size = 41, normalized size = 1.71 \begin{align*} \frac{x^{5} - 2 \, \log \left (x^{5} + 2\right )}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.238175, size = 17, normalized size = 0.71 \begin{align*} \frac{x^{5}}{5 b} - \frac{2 \log{\left (x^{5} + 2 \right )}}{5 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20889, size = 28, normalized size = 1.17 \begin{align*} \frac{x^{5}}{5 \, b} - \frac{2 \, \log \left ({\left | x^{5} + 2 \right |}\right )}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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