Optimal. Leaf size=26 \[ \frac{x^5}{5 b}-\frac{3 \log \left (b x^5+3\right )}{5 b^2} \]
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Rubi [A] time = 0.0164288, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{x^5}{5 b}-\frac{3 \log \left (b x^5+3\right )}{5 b^2} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^9}{3+b x^5} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{x}{3+b x} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (\frac{1}{b}-\frac{3}{b (3+b x)}\right ) \, dx,x,x^5\right )\\ &=\frac{x^5}{5 b}-\frac{3 \log \left (3+b x^5\right )}{5 b^2}\\ \end{align*}
Mathematica [A] time = 0.0037522, size = 26, normalized size = 1. \[ \frac{x^5}{5 b}-\frac{3 \log \left (b x^5+3\right )}{5 b^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 23, normalized size = 0.9 \begin{align*}{\frac{{x}^{5}}{5\,b}}-{\frac{3\,\ln \left ( b{x}^{5}+3 \right ) }{5\,{b}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01605, size = 30, normalized size = 1.15 \begin{align*} \frac{x^{5}}{5 \, b} - \frac{3 \, \log \left (b x^{5} + 3\right )}{5 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68095, size = 49, normalized size = 1.88 \begin{align*} \frac{b x^{5} - 3 \, \log \left (b x^{5} + 3\right )}{5 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.428499, size = 20, normalized size = 0.77 \begin{align*} \frac{x^{5}}{5 b} - \frac{3 \log{\left (b x^{5} + 3 \right )}}{5 b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.44173, size = 31, normalized size = 1.19 \begin{align*} \frac{x^{5}}{5 \, b} - \frac{3 \, \log \left ({\left | b x^{5} + 3 \right |}\right )}{5 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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