Optimal. Leaf size=23 \[ -\frac {2 \sqrt {a x^3+b x^4}}{a x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\frac {2 \sqrt {a x^3+b x^4}}{a x^2} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.91 \begin {gather*} -\frac {2 \sqrt {x^3 (a+b x)}}{a x^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.14, size = 23, normalized size = 1.00 \begin {gather*} -\frac {2 \sqrt {a x^3+b x^4}}{a x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 21, normalized size = 0.91 \begin {gather*} -\frac {2 \, \sqrt {b x^{4} + a x^{3}}}{a x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 27, normalized size = 1.17 \begin {gather*} \frac {2}{{\left (\sqrt {b} x - \sqrt {b x^{2} + a x}\right )} \mathrm {sgn}\relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 25, normalized size = 1.09 \begin {gather*} -\frac {2 \left (b x +a \right ) x}{\sqrt {b \,x^{4}+a \,x^{3}}\, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt {b x^{4} + a x^{3}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.14, size = 21, normalized size = 0.91 \begin {gather*} -\frac {2\,\sqrt {b\,x^4+a\,x^3}}{a\,x^2} \end {gather*}
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 \begin {gather*} \int \frac {1}{\sqrt {a x^{3} + b x^{4}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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