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 = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.00, 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 43
Rule 266
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*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ \frac {x^5}{5 b}-\frac {2 \log \left (x^5+2\right )}{5 b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 17, normalized size = 0.71 \[ \frac {x^{5} - 2 \, \log \left (x^{5} + 2\right )}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 21, normalized size = 0.88 \[ \frac {x^{5}}{5 \, b} - \frac {2 \, \log \left ({\left | x^{5} + 2 \right |}\right )}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 0.88 \[ \frac {x^{5}}{5 b}-\frac {2 \ln \left (x^{5}+2\right )}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.97, size = 20, normalized size = 0.83 \[ \frac {x^{5}}{5 \, b} - \frac {2 \, \log \left (x^{5} + 2\right )}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 19, normalized size = 0.79 \[ -\frac {2\,\ln \left (x^5+2\right )-x^5}{5\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 17, normalized size = 0.71 \[ \frac {x^{5}}{5 b} - \frac {2 \log {\left (x^{5} + 2 \right )}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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