Optimal. Leaf size=11 \[ -\frac {9}{x}+x+6 \log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {14}
\begin {gather*} x-\frac {9}{x}+6 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {9+6 x+x^2}{x^2} \, dx &=\int \left (1+\frac {9}{x^2}+\frac {6}{x}\right ) \, dx\\ &=-\frac {9}{x}+x+6 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} -\frac {9}{x}+x+6 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 12, normalized size = 1.09
method | result | size |
default | \(-\frac {9}{x}+x +6 \ln \left (x \right )\) | \(12\) |
risch | \(-\frac {9}{x}+x +6 \ln \left (x \right )\) | \(12\) |
norman | \(\frac {x^{2}-9}{x}+6 \ln \left (x \right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 11, normalized size = 1.00 \begin {gather*} x - \frac {9}{x} + 6 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.44, size = 14, normalized size = 1.27 \begin {gather*} \frac {x^{2} + 6 \, x \log \left (x\right ) - 9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 8, normalized size = 0.73 \begin {gather*} x + 6 \log {\left (x \right )} - \frac {9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.84, size = 12, normalized size = 1.09 \begin {gather*} x - \frac {9}{x} + 6 \, \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 = 1.00 \begin {gather*} x+6\,\ln \left (x\right )-\frac {9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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