Optimal. Leaf size=15 \[ \frac {1}{1-x}-\frac {2}{(1+x)^2} \]
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Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {1634}
\begin {gather*} \frac {1}{1-x}-\frac {2}{(x+1)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 1634
Rubi steps
\begin {align*} \int \frac {5-5 x+7 x^2+x^3}{(-1+x)^2 (1+x)^3} \, dx &=\int \left (\frac {1}{(-1+x)^2}+\frac {4}{(1+x)^3}\right ) \, dx\\ &=\frac {1}{1-x}-\frac {2}{(1+x)^2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} -\frac {1}{-1+x}-\frac {2}{(1+x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.23, size = 16, normalized size = 1.07
method | result | size |
default | \(-\frac {1}{-1+x}-\frac {2}{\left (1+x \right )^{2}}\) | \(16\) |
gosper | \(-\frac {x^{2}+4 x -1}{\left (-1+x \right ) \left (1+x \right )^{2}}\) | \(21\) |
norman | \(\frac {-x^{2}-4 x +1}{\left (1+x \right )^{2} \left (-1+x \right )}\) | \(22\) |
risch | \(\frac {-x^{2}-4 x +1}{\left (1+x \right )^{2} \left (-1+x \right )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 23, normalized size = 1.53 \begin {gather*} -\frac {x^{2} + 4 \, x - 1}{x^{3} + x^{2} - x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 23, normalized size = 1.53 \begin {gather*} -\frac {x^{2} + 4 \, x - 1}{x^{3} + x^{2} - x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 17, normalized size = 1.13 \begin {gather*} \frac {- x^{2} - 4 x + 1}{x^{3} + x^{2} - x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.35, size = 30, normalized size = 2.00 \begin {gather*} -\frac {1}{x - 1} + \frac {\frac {4}{x - 1} + 1}{2 \, {\left (\frac {2}{x - 1} + 1\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.09, size = 15, normalized size = 1.00 \begin {gather*} -\frac {1}{x-1}-\frac {2}{{\left (x+1\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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