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 = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.61, size = 27, normalized size = 0.82 \[ -\frac {20 \, B b x^{2} + 12 \, A a + 15 \, {\left (B a + A b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.27, size = 27, normalized size = 0.82 \[ -\frac {20 \, B b x^{2} + 15 \, B a x + 15 \, A b x + 12 \, A a}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 28, normalized size = 0.85 \[ -\frac {B b}{3 x^{3}}-\frac {A a}{5 x^{5}}-\frac {A b +B a}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.07, size = 27, normalized size = 0.82 \[ -\frac {20 \, B b x^{2} + 12 \, A a + 15 \, {\left (B a + A b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.85 \[ -\frac {\frac {B\,b\,x^2}{3}+\left (\frac {A\,b}{4}+\frac {B\,a}{4}\right )\,x+\frac {A\,a}{5}}{x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.48, size = 31, normalized size = 0.94 \[ \frac {- 12 A a - 20 B b x^{2} + x \left (- 15 A b - 15 B a\right )}{60 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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