Optimal. Leaf size=23 \[ -\frac {2 \sqrt {a x+b x^4}}{3 a x^2} \]
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Rubi [A] time = 0.03, antiderivative size = 23, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 1.00 \[ -\frac {2 \sqrt {x \left (a+b x^3\right )}}{3 a x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 19, normalized size = 0.83 \[ -\frac {2 \, \sqrt {b x^{4} + a x}}{3 \, a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 14, normalized size = 0.61 \[ -\frac {2 \, \sqrt {b + \frac {a}{x^{3}}}}{3 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 27, normalized size = 1.17 \[ -\frac {2 \left (b \,x^{3}+a \right )}{3 \sqrt {b \,x^{4}+a x}\, a x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.46, size = 26, normalized size = 1.13 \[ -\frac {2 \, {\left (b x^{4} + a x\right )}}{3 \, \sqrt {b x^{3} + a} a x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.13, size = 19, normalized size = 0.83 \[ -\frac {2\,\sqrt {b\,x^4+a\,x}}{3\,a\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \sqrt {x \left (a + b x^{3}\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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