Optimal. Leaf size=25 \[ -7-\left (-3+\frac {5}{x}\right ) x^2+\frac {x}{1+x}-\log (x) \]
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Rubi [A] time = 0.04, antiderivative size = 20, normalized size of antiderivative = 0.80, number of steps used = 4, number of rules used = 3, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1594, 27, 1620} \begin {gather*} 3 x^2-5 x-\frac {1}{x+1}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1594
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1-6 x-5 x^2+7 x^3+6 x^4}{x \left (1+2 x+x^2\right )} \, dx\\ &=\int \frac {-1-6 x-5 x^2+7 x^3+6 x^4}{x (1+x)^2} \, dx\\ &=\int \left (-5-\frac {1}{x}+6 x+\frac {1}{(1+x)^2}\right ) \, dx\\ &=-5 x+3 x^2-\frac {1}{1+x}-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 0.80 \begin {gather*} -5 x+3 x^2-\frac {1}{1+x}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 28, normalized size = 1.12 \begin {gather*} \frac {3 \, x^{3} - 2 \, x^{2} - {\left (x + 1\right )} \log \relax (x) - 5 \, x - 1}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 21, normalized size = 0.84 \begin {gather*} 3 \, x^{2} - 5 \, x - \frac {1}{x + 1} - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 21, normalized size = 0.84
method | result | size |
default | \(3 x^{2}-5 x -\ln \relax (x )-\frac {1}{x +1}\) | \(21\) |
risch | \(3 x^{2}-5 x -\ln \relax (x )-\frac {1}{x +1}\) | \(21\) |
norman | \(\frac {3 x^{3}-2 x^{2}+4}{x +1}-\ln \relax (x )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 20, normalized size = 0.80 \begin {gather*} 3 \, x^{2} - 5 \, x - \frac {1}{x + 1} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 20, normalized size = 0.80 \begin {gather*} 3\,x^2-\ln \relax (x)-\frac {1}{x+1}-5\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.60 \begin {gather*} 3 x^{2} - 5 x - \log {\relax (x )} - \frac {1}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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