Optimal. Leaf size=18 \[ \frac {\sqrt {16 x^2-9}}{9 x} \]
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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} \[ \frac {\sqrt {16 x^2-9}}{9 x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {1}{x^2 \sqrt {-9+16 x^2}} \, dx &=\frac {\sqrt {-9+16 x^2}}{9 x}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {\sqrt {16 x^2-9}}{9 x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 18, normalized size = 1.00 \[ \frac {4 \, x + \sqrt {16 \, x^{2} - 9}}{9 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 23, normalized size = 1.28 \[ \frac {8}{{\left (4 \, x - \sqrt {16 \, x^{2} - 9}\right )}^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 1.39 \[ \frac {\left (4 x -3\right ) \left (4 x +3\right )}{9 \sqrt {16 x^{2}-9}\, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 14, normalized size = 0.78 \[ \frac {\sqrt {16 \, x^{2} - 9}}{9 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 14, normalized size = 0.78 \[ \frac {\sqrt {16\,x^2-9}}{9\,x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.82, size = 37, normalized size = 2.06 \[ \begin {cases} \frac {4 i \sqrt {-1 + \frac {9}{16 x^{2}}}}{9} & \text {for}\: \frac {9}{16 \left |{x^{2}}\right |} > 1 \\\frac {4 \sqrt {1 - \frac {9}{16 x^{2}}}}{9} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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