Optimal. Leaf size=16 \[ -\frac {x}{25 \sqrt {4 x^2-25}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {191} \[ -\frac {x}{25 \sqrt {4 x^2-25}} \]
Antiderivative was successfully verified.
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Rule 191
Rubi steps
\begin {align*} \int \frac {1}{\left (-25+4 x^2\right )^{3/2}} \, dx &=-\frac {x}{25 \sqrt {-25+4 x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ -\frac {x}{25 \sqrt {4 x^2-25}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.40, size = 30, normalized size = 1.88 \[ -\frac {4 \, x^{2} + 2 \, \sqrt {4 \, x^{2} - 25} x - 25}{50 \, {\left (4 \, x^{2} - 25\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 12, normalized size = 0.75 \[ -\frac {x}{25 \, \sqrt {4 \, x^{2} - 25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 1.44 \[ -\frac {\left (2 x -5\right ) \left (2 x +5\right ) x}{25 \left (4 x^{2}-25\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 12, normalized size = 0.75 \[ -\frac {x}{25 \, \sqrt {4 \, x^{2} - 25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 12, normalized size = 0.75 \[ -\frac {x}{25\,\sqrt {4\,x^2-25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.78, size = 36, normalized size = 2.25 \[ \begin {cases} - \frac {x}{25 \sqrt {4 x^{2} - 25}} & \text {for}\: \frac {4 \left |{x^{2}}\right |}{25} > 1 \\\frac {i x}{25 \sqrt {25 - 4 x^{2}}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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