Optimal. Leaf size=68 \[ -\frac{a C+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{a B}{5 x^5}-\frac{A c+b C}{2 x^2}-\frac{b B}{3 x^3}-\frac{B c}{x}+c C \log (x) \]
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Rubi [A] time = 0.0482934, antiderivative size = 68, 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} \[ -\frac{a C+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{a B}{5 x^5}-\frac{A c+b C}{2 x^2}-\frac{b B}{3 x^3}-\frac{B c}{x}+c C \log (x) \]
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^7} \, dx &=\int \left (\frac{a A}{x^7}+\frac{a B}{x^6}+\frac{A b+a C}{x^5}+\frac{b B}{x^4}+\frac{A c+b C}{x^3}+\frac{B c}{x^2}+\frac{c C}{x}\right ) \, dx\\ &=-\frac{a A}{6 x^6}-\frac{a B}{5 x^5}-\frac{A b+a C}{4 x^4}-\frac{b B}{3 x^3}-\frac{A c+b C}{2 x^2}-\frac{B c}{x}+c C \log (x)\\ \end{align*}
Mathematica [A] time = 0.0475365, size = 68, normalized size = 1. \[ c C \log (x)-\frac{a (10 A+3 x (4 B+5 C x))+5 x^2 \left (3 A \left (b+2 c x^2\right )+2 x \left (2 b B+3 b C x+6 B c x^2\right )\right )}{60 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 63, normalized size = 0.9 \begin{align*} -{\frac{Bc}{x}}-{\frac{Ac}{2\,{x}^{2}}}-{\frac{bC}{2\,{x}^{2}}}-{\frac{Ba}{5\,{x}^{5}}}-{\frac{Ab}{4\,{x}^{4}}}-{\frac{aC}{4\,{x}^{4}}}-{\frac{Aa}{6\,{x}^{6}}}-{\frac{Bb}{3\,{x}^{3}}}+cC\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967971, size = 80, normalized size = 1.18 \begin{align*} C c \log \left (x\right ) - \frac{60 \, B c x^{5} + 20 \, B b x^{3} + 30 \,{\left (C b + A c\right )} x^{4} + 12 \, B a x + 15 \,{\left (C a + A b\right )} x^{2} + 10 \, A a}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27163, size = 159, normalized size = 2.34 \begin{align*} \frac{60 \, C c x^{6} \log \left (x\right ) - 60 \, B c x^{5} - 20 \, B b x^{3} - 30 \,{\left (C b + A c\right )} x^{4} - 12 \, B a x - 15 \,{\left (C a + A b\right )} x^{2} - 10 \, A a}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 16.138, size = 66, normalized size = 0.97 \begin{align*} C c \log{\left (x \right )} - \frac{10 A a + 12 B a x + 20 B b x^{3} + 60 B c x^{5} + x^{4} \left (30 A c + 30 C b\right ) + x^{2} \left (15 A b + 15 C a\right )}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09615, size = 81, normalized size = 1.19 \begin{align*} C c \log \left ({\left | x \right |}\right ) - \frac{60 \, B c x^{5} + 20 \, B b x^{3} + 30 \,{\left (C b + A c\right )} x^{4} + 12 \, B a x + 15 \,{\left (C a + A b\right )} x^{2} + 10 \, A a}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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