Optimal. Leaf size=1 \[ x \]
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Rubi [A]
time = 0.00, antiderivative size = 1, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {21, 8}
\begin {gather*} x \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 21
Rubi steps
\begin {align*} \int \frac {\left (1-x^2\right )^2}{\left (-1+x^2\right )^2} \, dx &=\int 1 \, dx\\ &=x\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 2, normalized size = 2.00
method | result | size |
default | \(x\) | \(2\) |
risch | \(x\) | \(2\) |
norman | \(\frac {x^{3}-x}{x^{2}-1}\) | \(16\) |
meijerg | \(-\frac {i \left (\frac {i x \left (-10 x^{2}+15\right )}{-5 x^{2}+5}-3 i \arctanh \left (x \right )\right )}{2}-i \left (-\frac {i x}{-x^{2}+1}+i \arctanh \left (x \right )\right )-\frac {i \left (\frac {2 i x}{-2 x^{2}+2}+i \arctanh \left (x \right )\right )}{2}\) | \(75\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.84, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 0, normalized size = 0.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.32, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.00, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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