Optimal. Leaf size=33 \[ -\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{b B}{3 x^3} \]
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Rubi [A] time = 0.0131032, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {76} \[ -\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{b B}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x) (A+B x)}{x^6} \, dx &=\int \left (\frac{a A}{x^6}+\frac{A b+a B}{x^5}+\frac{b B}{x^4}\right ) \, dx\\ &=-\frac{a A}{5 x^5}-\frac{A b+a B}{4 x^4}-\frac{b B}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0097122, size = 31, normalized size = 0.94 \[ -\frac{3 a (4 A+5 B x)+5 b x (3 A+4 B x)}{60 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 28, normalized size = 0.9 \begin{align*} -{\frac{Bb}{3\,{x}^{3}}}-{\frac{Aa}{5\,{x}^{5}}}-{\frac{Ab+Ba}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01521, size = 36, normalized size = 1.09 \begin{align*} -\frac{20 \, B b x^{2} + 12 \, A a + 15 \,{\left (B a + A b\right )} x}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.84178, size = 70, normalized size = 2.12 \begin{align*} -\frac{20 \, B b x^{2} + 12 \, A a + 15 \,{\left (B a + A b\right )} x}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.604936, size = 31, normalized size = 0.94 \begin{align*} - \frac{12 A a + 20 B b x^{2} + x \left (15 A b + 15 B a\right )}{60 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.28133, size = 36, normalized size = 1.09 \begin{align*} -\frac{20 \, B b x^{2} + 15 \, B a x + 15 \, A b x + 12 \, A a}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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