Optimal. Leaf size=12 \[ \frac {x}{a-b x^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {391}
\begin {gather*} \frac {x}{a-b x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 391
Rubi steps
\begin {align*} \int \frac {a+b x^2}{\left (-a+b x^2\right )^2} \, dx &=\frac {x}{a-b x^2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 1.17 \begin {gather*} -\frac {x}{-a+b x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 13, normalized size = 1.08
method | result | size |
gosper | \(\frac {x}{-b \,x^{2}+a}\) | \(13\) |
default | \(\frac {x}{-b \,x^{2}+a}\) | \(13\) |
norman | \(\frac {x}{-b \,x^{2}+a}\) | \(13\) |
risch | \(\frac {x}{-b \,x^{2}+a}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 1.17 \begin {gather*} -\frac {x}{b x^{2} - a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.12, size = 14, normalized size = 1.17 \begin {gather*} -\frac {x}{b x^{2} - a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 8, normalized size = 0.67 \begin {gather*} - \frac {x}{- a + b x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.18, size = 14, normalized size = 1.17 \begin {gather*} -\frac {x}{b x^{2} - a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 12, normalized size = 1.00 \begin {gather*} \frac {x}{a-b\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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