Optimal. Leaf size=55 \[ -\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{4 x^4}-\frac{b^2 B}{3 x^3} \]
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Rubi [A] time = 0.0224797, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {76} \[ -\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{4 x^4}-\frac{b^2 B}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x)^2 (A+B x)}{x^7} \, dx &=\int \left (\frac{a^2 A}{x^7}+\frac{a (2 A b+a B)}{x^6}+\frac{b (A b+2 a B)}{x^5}+\frac{b^2 B}{x^4}\right ) \, dx\\ &=-\frac{a^2 A}{6 x^6}-\frac{a (2 A b+a B)}{5 x^5}-\frac{b (A b+2 a B)}{4 x^4}-\frac{b^2 B}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0159978, size = 50, normalized size = 0.91 \[ -\frac{2 a^2 (5 A+6 B x)+6 a b x (4 A+5 B x)+5 b^2 x^2 (3 A+4 B x)}{60 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 48, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{2}}{6\,{x}^{6}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{5\,{x}^{5}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{4\,{x}^{4}}}-{\frac{B{b}^{2}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01634, size = 69, normalized size = 1.25 \begin{align*} -\frac{20 \, B b^{2} x^{3} + 10 \, A a^{2} + 15 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 12 \,{\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.838, size = 120, normalized size = 2.18 \begin{align*} -\frac{20 \, B b^{2} x^{3} + 10 \, A a^{2} + 15 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 12 \,{\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.2808, size = 54, normalized size = 0.98 \begin{align*} - \frac{10 A a^{2} + 20 B b^{2} x^{3} + x^{2} \left (15 A b^{2} + 30 B a b\right ) + x \left (24 A a b + 12 B a^{2}\right )}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19253, size = 69, normalized size = 1.25 \begin{align*} -\frac{20 \, B b^{2} x^{3} + 30 \, B a b x^{2} + 15 \, A b^{2} x^{2} + 12 \, B a^{2} x + 24 \, A a b x + 10 \, A a^{2}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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