Optimal. Leaf size=16 \[ -\frac {\log \left (a-b x^2\right )}{2 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {260} \[ -\frac {\log \left (a-b x^2\right )}{2 b} \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin {align*} \int \frac {x}{a-b x^2} \, dx &=-\frac {\log \left (a-b x^2\right )}{2 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ -\frac {\log \left (a-b x^2\right )}{2 b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 15, normalized size = 0.94 \[ -\frac {\log \left (b x^{2} - a\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.61, size = 16, normalized size = 1.00 \[ -\frac {\log \left ({\left | b x^{2} - a \right |}\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 1.00 \[ -\frac {\ln \left (b \,x^{2}-a \right )}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 15, normalized size = 0.94 \[ -\frac {\log \left (b x^{2} - a\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.94 \[ -\frac {\ln \left (b\,x^2-a\right )}{2\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 12, normalized size = 0.75 \[ - \frac {\log {\left (- a + b x^{2} \right )}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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