Optimal. Leaf size=15 \[ -\frac {4}{3}-x+\frac {1}{x^2+\log (x)} \]
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Rubi [A]
time = 0.23, antiderivative size = 12, normalized size of antiderivative = 0.80, number of steps
used = 4, number of rules used = 3, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {6820, 6874,
6818} \begin {gather*} \frac {1}{x^2+\log (x)}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1-2 x^2-x^5-2 x^3 \log (x)-x \log ^2(x)}{x \left (x^2+\log (x)\right )^2} \, dx\\ &=\int \left (-1+\frac {-1-2 x^2}{x \left (x^2+\log (x)\right )^2}\right ) \, dx\\ &=-x+\int \frac {-1-2 x^2}{x \left (x^2+\log (x)\right )^2} \, dx\\ &=-x+\frac {1}{x^2+\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 12, normalized size = 0.80 \begin {gather*} -x+\frac {1}{x^2+\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 20, normalized size = 1.33
method | result | size |
risch | \(-x +\frac {1}{\ln \left (x \right )+x^{2}}\) | \(13\) |
default | \(-\frac {-1+x^{3}+x \ln \left (x \right )}{\ln \left (x \right )+x^{2}}\) | \(20\) |
norman | \(\frac {1-x^{3}-x \ln \left (x \right )}{\ln \left (x \right )+x^{2}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 19, normalized size = 1.27 \begin {gather*} -\frac {x^{3} + x \log \left (x\right ) - 1}{x^{2} + \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 19, normalized size = 1.27 \begin {gather*} -\frac {x^{3} + x \log \left (x\right ) - 1}{x^{2} + \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.53 \begin {gather*} - x + \frac {1}{x^{2} + \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 12, normalized size = 0.80 \begin {gather*} -x + \frac {1}{x^{2} + \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.45, size = 12, normalized size = 0.80 \begin {gather*} \frac {1}{\ln \left (x\right )+x^2}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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