Optimal. Leaf size=25 \[ \frac{1}{8} \log \left (320 x^4+80 x^3-12 x^2+24 x+9\right ) \]
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Rubi [A] time = 0.0226836, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 38, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.026, Rules used = {1587} \[ \frac{1}{8} \log \left (320 x^4+80 x^3-12 x^2+24 x+9\right ) \]
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin{align*} \int \frac{3-3 x+30 x^2+160 x^3}{9+24 x-12 x^2+80 x^3+320 x^4} \, dx &=\frac{1}{8} \log \left (9+24 x-12 x^2+80 x^3+320 x^4\right )\\ \end{align*}
Mathematica [A] time = 0.0081255, size = 25, normalized size = 1. \[ \frac{1}{8} \log \left (320 x^4+80 x^3-12 x^2+24 x+9\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 24, normalized size = 1. \begin{align*}{\frac{\ln \left ( 320\,{x}^{4}+80\,{x}^{3}-12\,{x}^{2}+24\,x+9 \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936682, size = 31, normalized size = 1.24 \begin{align*} \frac{1}{8} \, \log \left (320 \, x^{4} + 80 \, x^{3} - 12 \, x^{2} + 24 \, x + 9\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.30158, size = 63, normalized size = 2.52 \begin{align*} \frac{1}{8} \, \log \left (320 \, x^{4} + 80 \, x^{3} - 12 \, x^{2} + 24 \, x + 9\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.097344, size = 22, normalized size = 0.88 \begin{align*} \frac{\log{\left (320 x^{4} + 80 x^{3} - 12 x^{2} + 24 x + 9 \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07841, size = 31, normalized size = 1.24 \begin{align*} \frac{1}{8} \, \log \left (320 \, x^{4} + 80 \, x^{3} - 12 \, x^{2} + 24 \, x + 9\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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