Optimal. Leaf size=15 \[ 2 \log (1-x)+3 \log (3+x) \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {646, 31}
\begin {gather*} 2 \log (1-x)+3 \log (x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 646
Rubi steps
\begin {align*} \int \frac {3+5 x}{-3+2 x+x^2} \, dx &=2 \int \frac {1}{-1+x} \, dx+3 \int \frac {1}{3+x} \, dx\\ &=2 \log (1-x)+3 \log (3+x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} 2 \log (1-x)+3 \log (3+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 14, normalized size = 0.93
method | result | size |
default | \(2 \ln \left (-1+x \right )+3 \ln \left (3+x \right )\) | \(14\) |
norman | \(2 \ln \left (-1+x \right )+3 \ln \left (3+x \right )\) | \(14\) |
risch | \(2 \ln \left (-1+x \right )+3 \ln \left (3+x \right )\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.98, size = 13, normalized size = 0.87 \begin {gather*} 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.23, size = 13, normalized size = 0.87 \begin {gather*} 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.80 \begin {gather*} 2 \log {\left (x - 1 \right )} + 3 \log {\left (x + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 15, normalized size = 1.00 \begin {gather*} 3 \, \log \left ({\left | x + 3 \right |}\right ) + 2 \, \log \left ({\left | x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 13, normalized size = 0.87 \begin {gather*} 2\,\ln \left (x-1\right )+3\,\ln \left (x+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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