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 = 0.04, antiderivative size = 65, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 65, normalized size = 1.00 \[ \frac {1}{2} x^2 (a C+A b)+a A \log (x)+a B x+\frac {1}{4} x^4 (A c+b C)+\frac {1}{3} b B x^3+\frac {1}{5} B c x^5+\frac {1}{6} c C x^6 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 55, normalized size = 0.85 \[ \frac {1}{6} \, C c x^{6} + \frac {1}{5} \, B c x^{5} + \frac {1}{3} \, B b x^{3} + \frac {1}{4} \, {\left (C b + A c\right )} x^{4} + B a x + \frac {1}{2} \, {\left (C a + A b\right )} x^{2} + A a \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 60, normalized size = 0.92 \[ \frac {1}{6} \, C c x^{6} + \frac {1}{5} \, B c x^{5} + \frac {1}{4} \, C b x^{4} + \frac {1}{4} \, A c x^{4} + \frac {1}{3} \, B b x^{3} + \frac {1}{2} \, C a x^{2} + \frac {1}{2} \, A b x^{2} + B a x + A a \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 60, normalized size = 0.92 \[ \frac {C c \,x^{6}}{6}+\frac {B c \,x^{5}}{5}+\frac {A c \,x^{4}}{4}+\frac {C b \,x^{4}}{4}+\frac {B b \,x^{3}}{3}+\frac {A b \,x^{2}}{2}+\frac {C a \,x^{2}}{2}+A a \ln \relax (x )+B a x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 55, normalized size = 0.85 \[ \frac {1}{6} \, C c x^{6} + \frac {1}{5} \, B c x^{5} + \frac {1}{3} \, B b x^{3} + \frac {1}{4} \, {\left (C b + A c\right )} x^{4} + B a x + \frac {1}{2} \, {\left (C a + A b\right )} x^{2} + A a \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 57, normalized size = 0.88 \[ x^2\,\left (\frac {A\,b}{2}+\frac {C\,a}{2}\right )+x^4\,\left (\frac {A\,c}{4}+\frac {C\,b}{4}\right )+B\,a\,x+\frac {B\,b\,x^3}{3}+\frac {B\,c\,x^5}{5}+\frac {C\,c\,x^6}{6}+A\,a\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 63, normalized size = 0.97 \[ A a \log {\relax (x )} + B a x + \frac {B b x^{3}}{3} + \frac {B c x^{5}}{5} + \frac {C c x^{6}}{6} + x^{4} \left (\frac {A c}{4} + \frac {C b}{4}\right ) + x^{2} \left (\frac {A b}{2} + \frac {C a}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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