Optimal. Leaf size=15 \[ -\frac {1}{2 x^2}-\frac {1}{x}+\log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} -\frac {1}{2 x^2}-\frac {1}{x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (\frac {1}{x^3}+\frac {1}{x^2}+\frac {1}{x}\right ) \, dx &=-\frac {1}{2 x^2}-\frac {1}{x}+\log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {1}{2 x^2}-\frac {1}{x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 14, normalized size = 0.93
method | result | size |
norman | \(\frac {-\frac {1}{2}-x}{x^{2}}+\ln \left (x \right )\) | \(13\) |
default | \(-\frac {1}{2 x^{2}}-\frac {1}{x}+\ln \left (x \right )\) | \(14\) |
risch | \(-\frac {1}{2 x^{2}}-\frac {1}{x}+\ln \left (x \right )\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.87 \begin {gather*} -\frac {1}{x} - \frac {1}{2 \, 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 = 0.86, size = 17, normalized size = 1.13 \begin {gather*} \frac {2 \, x^{2} \log \left (x\right ) - 2 \, x - 1}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 0.93 \begin {gather*} \log {\left (x \right )} + \frac {- 2 x - 1}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.15, size = 14, normalized size = 0.93 \begin {gather*} -\frac {1}{x} - \frac {1}{2 \, x^{2}} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 11, normalized size = 0.73 \begin {gather*} \ln \left (x\right )-\frac {x+\frac {1}{2}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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