Optimal. Leaf size=10 \[ x-2 \log (2 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {43} \[ x-2 \log (2 x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {-1+2 x}{3+2 x} \, dx &=\int \left (1-\frac {4}{3+2 x}\right ) \, dx\\ &=x-2 \log (3+2 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ x-2 \log (2 x+3) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.00, size = 10, normalized size = 1.00 \[ x-2 \log (2 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 10, normalized size = 1.00 \[ x - 2 \, \log \left (2 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 11, normalized size = 1.10 \[ x - 2 \, \log \left ({\left | 2 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 11, normalized size = 1.10
method | result | size |
default | \(x -2 \ln \left (3+2 x \right )\) | \(11\) |
norman | \(x -2 \ln \left (3+2 x \right )\) | \(11\) |
meijerg | \(-2 \ln \left (1+\frac {2 x}{3}\right )+x\) | \(11\) |
risch | \(x -2 \ln \left (3+2 x \right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 10, normalized size = 1.00 \[ x - 2 \, \log \left (2 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 8, normalized size = 0.80 \[ x-2\,\ln \left (x+\frac {3}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.80 \[ x - 2 \log {\left (2 x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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