Optimal. Leaf size=63 \[ -\frac{a C+A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{a B}{4 x^4}-\frac{A c+b C}{x}-\frac{b B}{2 x^2}+B c \log (x)+c C x \]
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Rubi [A] time = 0.0516926, antiderivative size = 63, 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} \[ -\frac{a C+A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{a B}{4 x^4}-\frac{A c+b C}{x}-\frac{b B}{2 x^2}+B c \log (x)+c C x \]
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^6} \, dx &=\int \left (c C+\frac{a A}{x^6}+\frac{a B}{x^5}+\frac{A b+a C}{x^4}+\frac{b B}{x^3}+\frac{A c+b C}{x^2}+\frac{B c}{x}\right ) \, dx\\ &=-\frac{a A}{5 x^5}-\frac{a B}{4 x^4}-\frac{A b+a C}{3 x^3}-\frac{b B}{2 x^2}-\frac{A c+b C}{x}+c C x+B c \log (x)\\ \end{align*}
Mathematica [A] time = 0.0584929, size = 63, normalized size = 1. \[ B c \log (x)-\frac{12 a A+5 a x (3 B+4 C x)+20 A x^2 \left (b+3 c x^2\right )+30 b x^3 (B+2 C x)-60 c C x^6}{60 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 60, normalized size = 1. \begin{align*} cCx-{\frac{Ac}{x}}-{\frac{bC}{x}}-{\frac{Bb}{2\,{x}^{2}}}-{\frac{Aa}{5\,{x}^{5}}}-{\frac{Ba}{4\,{x}^{4}}}-{\frac{Ab}{3\,{x}^{3}}}-{\frac{aC}{3\,{x}^{3}}}+Bc\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.952459, size = 76, normalized size = 1.21 \begin{align*} C c x + B c \log \left (x\right ) - \frac{30 \, B b x^{3} + 60 \,{\left (C b + A c\right )} x^{4} + 15 \, B a x + 20 \,{\left (C a + A b\right )} x^{2} + 12 \, A a}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.20798, size = 159, normalized size = 2.52 \begin{align*} \frac{60 \, C c x^{6} + 60 \, B c x^{5} \log \left (x\right ) - 30 \, B b x^{3} - 60 \,{\left (C b + A c\right )} x^{4} - 15 \, B a x - 20 \,{\left (C a + A b\right )} x^{2} - 12 \, A a}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 8.34503, size = 63, normalized size = 1. \begin{align*} B c \log{\left (x \right )} + C c x - \frac{12 A a + 15 B a x + 30 B b x^{3} + x^{4} \left (60 A c + 60 C b\right ) + x^{2} \left (20 A b + 20 C a\right )}{60 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09146, size = 77, normalized size = 1.22 \begin{align*} C c x + B c \log \left ({\left | x \right |}\right ) - \frac{30 \, B b x^{3} + 60 \,{\left (C b + A c\right )} x^{4} + 15 \, B a x + 20 \,{\left (C a + A b\right )} x^{2} + 12 \, A a}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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