Optimal. Leaf size=18 \[ \frac {\left (-4 x^2-9\right )^{3/2}}{27 x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 18, 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 = {264} \[ \frac {\left (-4 x^2-9\right )^{3/2}}{27 x^3} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\sqrt {-9-4 x^2}}{x^4} \, dx &=\frac {\left (-9-4 x^2\right )^{3/2}}{27 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {\left (-4 x^2-9\right )^{3/2}}{27 x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 14, normalized size = 0.78 \[ \frac {{\left (-4 \, x^{2} - 9\right )}^{\frac {3}{2}}}{27 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {-4 \, x^{2} - 9}}{x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.83 \[ \frac {\left (-4 x^{2}-9\right )^{\frac {3}{2}}}{27 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.89, size = 14, normalized size = 0.78 \[ \frac {{\left (-4 \, x^{2} - 9\right )}^{\frac {3}{2}}}{27 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.74, size = 31, normalized size = 1.72 \[ -\frac {4\,x^2\,\sqrt {-4\,x^2-9}+9\,\sqrt {-4\,x^2-9}}{27\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 1.00, size = 37, normalized size = 2.06 \[ - \frac {8 i \sqrt {1 + \frac {9}{4 x^{2}}}}{27} - \frac {2 i \sqrt {1 + \frac {9}{4 x^{2}}}}{3 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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