Optimal. Leaf size=10 \[ \log \left (a x+b x^3\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {1587} \[ \log \left (a x+b x^3\right ) \]
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {align*} \int \frac {a+3 b x^2}{a x+b x^3} \, dx &=\log \left (a x+b x^3\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.10 \[ \log \left (a+b x^2\right )+\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 10, normalized size = 1.00 \[ \log \left (b x^{3} + a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 11, normalized size = 1.10 \[ \log \left ({\left | b x^{3} + a x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 1.10 \[ \ln \left (\left (b \,x^{2}+a \right ) x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 10, normalized size = 1.00 \[ \log \left (b x^{3} + a x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 10, normalized size = 1.00 \[ \ln \left (b\,x^3+a\,x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 8, normalized size = 0.80 \[ \log {\left (a x + b x^{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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