Optimal. Leaf size=23 \[ -\frac{2 \sqrt{a x+b x^4}}{3 a x^2} \]
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Rubi [A] time = 0.0337861, 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 = {2014} \[ -\frac{2 \sqrt{a x+b x^4}}{3 a x^2} \]
Antiderivative was successfully verified.
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Rule 2014
Rubi steps
\begin{align*} \int \frac{1}{x^2 \sqrt{a x+b x^4}} \, dx &=-\frac{2 \sqrt{a x+b x^4}}{3 a x^2}\\ \end{align*}
Mathematica [A] time = 0.0106894, size = 23, normalized size = 1. \[ -\frac{2 \sqrt{x \left (a+b x^3\right )}}{3 a x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 27, normalized size = 1.2 \begin{align*} -{\frac{2\,b{x}^{3}+2\,a}{3\,ax}{\frac{1}{\sqrt{b{x}^{4}+ax}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06738, size = 35, normalized size = 1.52 \begin{align*} -\frac{2 \,{\left (b x^{4} + a x\right )}}{3 \, \sqrt{b x^{3} + a} a x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.26757, 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}{x^{2} \sqrt{x \left (a + b x^{3}\right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19666, size = 19, normalized size = 0.83 \begin{align*} -\frac{2 \, \sqrt{b + \frac{a}{x^{3}}}}{3 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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