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 = 0.05, antiderivative size = 63, 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} \begin {gather*} -\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 \end {gather*}
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*}
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Mathematica [A] time = 0.05, size = 63, normalized size = 1.00 \begin {gather*} 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} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )}{x^6} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.28, size = 62, normalized size = 0.98 \begin {gather*} \frac {60 \, C c x^{6} + 60 \, B c x^{5} \log \relax (x) - 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 57, normalized size = 0.90 \begin {gather*} 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 60, normalized size = 0.95 \begin {gather*} B c \ln \relax (x )+C c x -\frac {A c}{x}-\frac {C b}{x}-\frac {B b}{2 x^{2}}-\frac {A b}{3 x^{3}}-\frac {C a}{3 x^{3}}-\frac {B a}{4 x^{4}}-\frac {A a}{5 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.74, size = 56, normalized size = 0.89 \begin {gather*} C c x + B c \log \relax (x) - \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.78, size = 56, normalized size = 0.89 \begin {gather*} C\,c\,x-\frac {\left (A\,c+C\,b\right )\,x^4+\frac {B\,b\,x^3}{2}+\left (\frac {A\,b}{3}+\frac {C\,a}{3}\right )\,x^2+\frac {B\,a\,x}{4}+\frac {A\,a}{5}}{x^5}+B\,c\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.70, size = 66, normalized size = 1.05 \begin {gather*} B c \log {\relax (x )} + 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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