Optimal. Leaf size=15 \[ \frac{\sqrt{a+b x^2}}{b} \]
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Rubi [A] time = 0.0033684, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.074, Rules used = {5, 261} \[ \frac{\sqrt{a+b x^2}}{b} \]
Antiderivative was successfully verified.
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Rule 5
Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx &=\int \frac{x}{\sqrt{a+b x^2}} \, dx\\ &=\frac{\sqrt{a+b x^2}}{b}\\ \end{align*}
Mathematica [A] time = 0.0020604, size = 15, normalized size = 1. \[ \frac{\sqrt{a+b x^2}}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.041, size = 14, normalized size = 0.9 \begin{align*}{\frac{1}{b}\sqrt{b{x}^{2}+a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.9383, size = 18, normalized size = 1.2 \begin{align*} \frac{\sqrt{b x^{2} + a}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5682, size = 26, normalized size = 1.73 \begin{align*} \frac{\sqrt{b x^{2} + a}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.368195, size = 20, normalized size = 1.33 \begin{align*} \begin{cases} \frac{\sqrt{a + b x^{2}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 \sqrt{a}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12855, size = 18, normalized size = 1.2 \begin{align*} \frac{\sqrt{b x^{2} + a}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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