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 = 0.02, antiderivative size = 26, normalized size of antiderivative = 1.00, 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 43
Rule 266
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*}
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Mathematica [A] time = 0.00, size = 26, normalized size = 1.00 \[ \frac {x^5}{5 b}-\frac {3 \log \left (b x^5+3\right )}{5 b^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 21, normalized size = 0.81 \[ \frac {b x^{5} - 3 \, \log \left (b x^{5} + 3\right )}{5 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.67, size = 23, normalized size = 0.88 \[ \frac {x^{5}}{5 \, b} - \frac {3 \, \log \left ({\left | b x^{5} + 3 \right |}\right )}{5 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 0.88 \[ \frac {x^{5}}{5 b}-\frac {3 \ln \left (b \,x^{5}+3\right )}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.01, size = 22, normalized size = 0.85 \[ \frac {x^{5}}{5 \, b} - \frac {3 \, \log \left (b x^{5} + 3\right )}{5 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.02, size = 22, normalized size = 0.85 \[ -\frac {3\,\ln \left (b\,x^5+3\right )-b\,x^5}{5\,b^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 20, normalized size = 0.77 \[ \frac {x^{5}}{5 b} - \frac {3 \log {\left (b x^{5} + 3 \right )}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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