Optimal. Leaf size=13 \[ x^2-3 x+\log (2 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {697} \[ x^2-3 x+\log (2 x+3) \]
Antiderivative was successfully verified.
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Rule 697
Rubi steps
\begin {align*} \int \frac {-7+4 x^2}{3+2 x} \, dx &=\int \left (-3+2 x+\frac {2}{3+2 x}\right ) \, dx\\ &=-3 x+x^2+\log (3+2 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.23 \[ x^2-3 x+\log (2 x+3)-\frac {27}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 13, normalized size = 1.00 \[ x^{2} - 3 \, x + \log \left (2 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 14, normalized size = 1.08 \[ x^{2} - 3 \, x + \log \left ({\left | 2 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 1.08 \[ x^{2}-3 x +\ln \left (2 x +3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 13, normalized size = 1.00 \[ x^{2} - 3 \, x + \log \left (2 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.21, size = 11, normalized size = 0.85 \[ \ln \left (x+\frac {3}{2}\right )-3\,x+x^2 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 12, normalized size = 0.92 \[ x^{2} - 3 x + \log {\left (2 x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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