Optimal. Leaf size=23 \[ \frac {\log (x)}{a}-\frac {\log \left (a-b x^3\right )}{3 a} \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {266, 36, 29, 31} \[ \frac {\log (x)}{a}-\frac {\log \left (a-b x^3\right )}{3 a} \]
Antiderivative was successfully verified.
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Rule 29
Rule 31
Rule 36
Rule 266
Rubi steps
\begin {align*} \int \frac {1}{x \left (a-b x^3\right )} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {1}{x (a-b x)} \, dx,x,x^3\right )\\ &=\frac {\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,x^3\right )}{3 a}+\frac {b \operatorname {Subst}\left (\int \frac {1}{a-b x} \, dx,x,x^3\right )}{3 a}\\ &=\frac {\log (x)}{a}-\frac {\log \left (a-b x^3\right )}{3 a}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \[ \frac {\log (x)}{a}-\frac {\log \left (a-b x^3\right )}{3 a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 20, normalized size = 0.87 \[ -\frac {\log \left (b x^{3} - a\right ) - 3 \, \log \relax (x)}{3 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 24, normalized size = 1.04 \[ -\frac {\log \left ({\left | b x^{3} - a \right |}\right )}{3 \, a} + \frac {\log \left ({\left | x \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 1.00 \[ \frac {\ln \relax (x )}{a}-\frac {\ln \left (b \,x^{3}-a \right )}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 25, normalized size = 1.09 \[ -\frac {\log \left (b x^{3} - a\right )}{3 \, a} + \frac {\log \left (x^{3}\right )}{3 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 21, normalized size = 0.91 \[ \frac {\ln \relax (x)}{a}-\frac {\ln \left (a-b\,x^3\right )}{3\,a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 15, normalized size = 0.65 \[ \frac {\log {\relax (x )}}{a} - \frac {\log {\left (- \frac {a}{b} + x^{3} \right )}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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