Optimal. Leaf size=14 \[ \frac {1}{2-x}+\tan ^{-1}(2-x) \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.190, Rules used = {27, 693, 618, 204} \[ \frac {1}{2-x}+\tan ^{-1}(2-x) \]
Antiderivative was successfully verified.
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Rule 27
Rule 204
Rule 618
Rule 693
Rubi steps
\begin {align*} \int \frac {1}{\left (4-4 x+x^2\right ) \left (5-4 x+x^2\right )} \, dx &=\int \frac {1}{(-2+x)^2 \left (5-4 x+x^2\right )} \, dx\\ &=\frac {1}{2-x}-\int \frac {1}{5-4 x+x^2} \, dx\\ &=\frac {1}{2-x}+2 \operatorname {Subst}\left (\int \frac {1}{-4-x^2} \, dx,x,-4+2 x\right )\\ &=\frac {1}{2-x}+\tan ^{-1}(2-x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \[ \tan ^{-1}(2-x)-\frac {1}{x-2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 17, normalized size = 1.21 \[ -\frac {{\left (x - 2\right )} \arctan \left (x - 2\right ) + 1}{x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 14, normalized size = 1.00 \[ -\frac {1}{x - 2} - \arctan \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 15, normalized size = 1.07 \[ -\arctan \left (x -2\right )-\frac {1}{x -2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 14, normalized size = 1.00 \[ -\frac {1}{x - 2} - \arctan \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 14, normalized size = 1.00 \[ -\mathrm {atan}\left (x-2\right )-\frac {1}{x-2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 10, normalized size = 0.71 \[ - \operatorname {atan}{\left (x - 2 \right )} - \frac {1}{x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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