Optimal. Leaf size=15 \[ \frac {\log \left (a x^2+b\right )}{2 a} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {263, 260} \[ \frac {\log \left (a x^2+b\right )}{2 a} \]
Antiderivative was successfully verified.
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Rule 260
Rule 263
Rubi steps
\begin {align*} \int \frac {1}{\left (a+\frac {b}{x^2}\right ) x} \, dx &=\int \frac {x}{b+a x^2} \, dx\\ &=\frac {\log \left (b+a x^2\right )}{2 a}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {\log \left (a x^2+b\right )}{2 a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 13, normalized size = 0.87 \[ \frac {\log \left (a x^{2} + b\right )}{2 \, a} \]
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 \[ \frac {\log \left ({\left | a x^{2} + b \right |}\right )}{2 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.93 \[ \frac {\ln \left (a \,x^{2}+b \right )}{2 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.86, size = 13, normalized size = 0.87 \[ \frac {\log \left (a x^{2} + b\right )}{2 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.06, size = 13, normalized size = 0.87 \[ \frac {\ln \left (a\,x^2+b\right )}{2\,a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 10, normalized size = 0.67 \[ \frac {\log {\left (a x^{2} + b \right )}}{2 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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