Optimal. Leaf size=65 \[ \frac{1}{2} x^2 (a C+A b)+a A \log (x)+a B x+\frac{1}{4} x^4 (A c+b C)+\frac{1}{3} b B x^3+\frac{1}{5} B c x^5+\frac{1}{6} c C x^6 \]
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Rubi [A] time = 0.0400262, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038, Rules used = {1628} \[ \frac{1}{2} x^2 (a C+A b)+a A \log (x)+a B x+\frac{1}{4} x^4 (A c+b C)+\frac{1}{3} b B x^3+\frac{1}{5} B c x^5+\frac{1}{6} c C x^6 \]
Antiderivative was successfully verified.
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Rule 1628
Rubi steps
\begin{align*} \int \frac{\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x} \, dx &=\int \left (a B+\frac{a A}{x}+(A b+a C) x+b B x^2+(A c+b C) x^3+B c x^4+c C x^5\right ) \, dx\\ &=a B x+\frac{1}{2} (A b+a C) x^2+\frac{1}{3} b B x^3+\frac{1}{4} (A c+b C) x^4+\frac{1}{5} B c x^5+\frac{1}{6} c C x^6+a A \log (x)\\ \end{align*}
Mathematica [A] time = 0.015423, size = 65, normalized size = 1. \[ \frac{1}{2} x^2 (a C+A b)+a A \log (x)+a B x+\frac{1}{4} x^4 (A c+b C)+\frac{1}{3} b B x^3+\frac{1}{5} B c x^5+\frac{1}{6} c C x^6 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 60, normalized size = 0.9 \begin{align*}{\frac{cC{x}^{6}}{6}}+{\frac{Bc{x}^{5}}{5}}+{\frac{A{x}^{4}c}{4}}+{\frac{C{x}^{4}b}{4}}+{\frac{bB{x}^{3}}{3}}+{\frac{A{x}^{2}b}{2}}+{\frac{C{x}^{2}a}{2}}+aBx+aA\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.940837, size = 74, normalized size = 1.14 \begin{align*} \frac{1}{6} \, C c x^{6} + \frac{1}{5} \, B c x^{5} + \frac{1}{3} \, B b x^{3} + \frac{1}{4} \,{\left (C b + A c\right )} x^{4} + B a x + \frac{1}{2} \,{\left (C a + A b\right )} x^{2} + A a \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27108, size = 143, normalized size = 2.2 \begin{align*} \frac{1}{6} \, C c x^{6} + \frac{1}{5} \, B c x^{5} + \frac{1}{3} \, B b x^{3} + \frac{1}{4} \,{\left (C b + A c\right )} x^{4} + B a x + \frac{1}{2} \,{\left (C a + A b\right )} x^{2} + A a \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.449987, size = 63, normalized size = 0.97 \begin{align*} A a \log{\left (x \right )} + B a x + \frac{B b x^{3}}{3} + \frac{B c x^{5}}{5} + \frac{C c x^{6}}{6} + x^{4} \left (\frac{A c}{4} + \frac{C b}{4}\right ) + x^{2} \left (\frac{A b}{2} + \frac{C a}{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09484, size = 81, normalized size = 1.25 \begin{align*} \frac{1}{6} \, C c x^{6} + \frac{1}{5} \, B c x^{5} + \frac{1}{4} \, C b x^{4} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{2} \, C a x^{2} + \frac{1}{2} \, A b x^{2} + B a x + A a \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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