Optimal. Leaf size=23 \[ \frac{2 \sqrt{a x^2+b x^3}}{b x} \]
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Rubi [A] time = 0.0101149, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {1588} \[ \frac{2 \sqrt{a x^2+b x^3}}{b x} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{a x^2+b x^3}} \, dx &=\frac{2 \sqrt{a x^2+b x^3}}{b x}\\ \end{align*}
Mathematica [A] time = 0.0073949, size = 21, normalized size = 0.91 \[ \frac{2 \sqrt{x^2 (a+b x)}}{b x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 1.1 \begin{align*} 2\,{\frac{x \left ( bx+a \right ) }{b\sqrt{b{x}^{3}+a{x}^{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16918, size = 16, normalized size = 0.7 \begin{align*} \frac{2 \, \sqrt{b x + a}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.797656, size = 39, normalized size = 1.7 \begin{align*} \frac{2 \, \sqrt{b x^{3} + a x^{2}}}{b x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{\sqrt{x^{2} \left (a + b x\right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18953, size = 35, normalized size = 1.52 \begin{align*} \frac{2}{\sqrt{\frac{b}{x} + \frac{a}{x^{2}}} - \frac{\sqrt{a}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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