Optimal. Leaf size=15 \[ \frac {\log \left (a x^3+b\right )}{3 a} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1593, 260} \begin {gather*} \frac {\log \left (a x^3+b\right )}{3 a} \end {gather*}
Antiderivative was successfully verified.
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Rule 260
Rule 1593
Rubi steps
\begin {align*} \int \frac {1}{\frac {b}{x^2}+a x} \, dx &=\int \frac {x^2}{b+a x^3} \, dx\\ &=\frac {\log \left (b+a x^3\right )}{3 a}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {\log \left (a x^3+b\right )}{3 a} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\frac {b}{x^2}+a x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 13, normalized size = 0.87 \begin {gather*} \frac {\log \left (a x^{3} + b\right )}{3 \, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 0.93 \begin {gather*} \frac {\log \left ({\left | a x^{3} + b \right |}\right )}{3 \, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 0.93 \begin {gather*} \frac {\ln \left (a \,x^{3}+b \right )}{3 a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 13, normalized size = 0.87 \begin {gather*} \frac {\log \left (a x^{3} + b\right )}{3 \, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.12, size = 13, normalized size = 0.87 \begin {gather*} \frac {\ln \left (a\,x^3+b\right )}{3\,a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 10, normalized size = 0.67 \begin {gather*} \frac {\log {\left (a x^{3} + b \right )}}{3 a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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