Optimal. Leaf size=21 \[ \frac {x^2}{\frac {x}{16}+2 x^2}+\log (\log (4)) \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.52, number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {12, 27, 32} \begin {gather*} -\frac {1}{2 (32 x+1)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=16 \int \frac {1}{1+64 x+1024 x^2} \, dx\\ &=16 \int \frac {1}{(1+32 x)^2} \, dx\\ &=-\frac {1}{2 (1+32 x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.52 \begin {gather*} -\frac {1}{2 (1+32 x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 9, normalized size = 0.43 \begin {gather*} -\frac {1}{2 \, {\left (32 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 9, normalized size = 0.43 \begin {gather*} -\frac {1}{2 \, {\left (32 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.36, size = 8, normalized size = 0.38
method | result | size |
risch | \(-\frac {1}{64 \left (x +\frac {1}{32}\right )}\) | \(8\) |
gosper | \(-\frac {1}{2 \left (32 x +1\right )}\) | \(10\) |
default | \(-\frac {1}{2 \left (32 x +1\right )}\) | \(10\) |
norman | \(\frac {16 x}{32 x +1}\) | \(11\) |
meijerg | \(\frac {16 x}{32 x +1}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 9, normalized size = 0.43 \begin {gather*} -\frac {1}{2 \, {\left (32 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.43 \begin {gather*} -\frac {1}{64\,x+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.33 \begin {gather*} - \frac {16}{1024 x + 32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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