Optimal. Leaf size=23 \[ -\frac{2 \sqrt{a x^3+b x^4}}{a x^2} \]
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Rubi [A] time = 0.0050791, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {2000} \[ -\frac{2 \sqrt{a x^3+b x^4}}{a x^2} \]
Antiderivative was successfully verified.
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Rule 2000
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{a x^3+b x^4}} \, dx &=-\frac{2 \sqrt{a x^3+b x^4}}{a x^2}\\ \end{align*}
Mathematica [A] time = 0.0071141, size = 21, normalized size = 0.91 \[ -\frac{2 \sqrt{x^3 (a+b x)}}{a x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 25, normalized size = 1.1 \begin{align*} -2\,{\frac{x \left ( bx+a \right ) }{a\sqrt{b{x}^{4}+a{x}^{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{b x^{4} + a x^{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.622897, size = 43, normalized size = 1.87 \begin{align*} -\frac{2 \, \sqrt{b x^{4} + a x^{3}}}{a x^{2}} \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{1}{\sqrt{a x^{3} + b x^{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21362, size = 36, normalized size = 1.57 \begin{align*} \frac{2}{{\left (\sqrt{b} x - \sqrt{b x^{2} + a x}\right )} \mathrm{sgn}\left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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