Optimal. Leaf size=117 \[ -\frac{5 a^2 b^2 (a B+A b)}{4 x^8}-\frac{a^4 (a B+5 A b)}{10 x^{10}}-\frac{5 a^3 b (a B+2 A b)}{9 x^9}-\frac{a^5 A}{11 x^{11}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{6 x^6}-\frac{b^5 B}{5 x^5} \]
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Rubi [A] time = 0.0590868, antiderivative size = 117, 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} \[ -\frac{5 a^2 b^2 (a B+A b)}{4 x^8}-\frac{a^4 (a B+5 A b)}{10 x^{10}}-\frac{5 a^3 b (a B+2 A b)}{9 x^9}-\frac{a^5 A}{11 x^{11}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{6 x^6}-\frac{b^5 B}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x)^5 (A+B x)}{x^{12}} \, dx &=\int \left (\frac{a^5 A}{x^{12}}+\frac{a^4 (5 A b+a B)}{x^{11}}+\frac{5 a^3 b (2 A b+a B)}{x^{10}}+\frac{10 a^2 b^2 (A b+a B)}{x^9}+\frac{5 a b^3 (A b+2 a B)}{x^8}+\frac{b^4 (A b+5 a B)}{x^7}+\frac{b^5 B}{x^6}\right ) \, dx\\ &=-\frac{a^5 A}{11 x^{11}}-\frac{a^4 (5 A b+a B)}{10 x^{10}}-\frac{5 a^3 b (2 A b+a B)}{9 x^9}-\frac{5 a^2 b^2 (A b+a B)}{4 x^8}-\frac{5 a b^3 (A b+2 a B)}{7 x^7}-\frac{b^4 (A b+5 a B)}{6 x^6}-\frac{b^5 B}{5 x^5}\\ \end{align*}
Mathematica [A] time = 0.0278819, size = 107, normalized size = 0.91 \[ -\frac{1925 a^3 b^2 x^2 (8 A+9 B x)+2475 a^2 b^3 x^3 (7 A+8 B x)+770 a^4 b x (9 A+10 B x)+126 a^5 (10 A+11 B x)+1650 a b^4 x^4 (6 A+7 B x)+462 b^5 x^5 (5 A+6 B x)}{13860 x^{11}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 104, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{5}}{11\,{x}^{11}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{10\,{x}^{10}}}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{9\,{x}^{9}}}-{\frac{5\,{b}^{2}{a}^{2} \left ( Ab+Ba \right ) }{4\,{x}^{8}}}-{\frac{5\,a{b}^{3} \left ( Ab+2\,Ba \right ) }{7\,{x}^{7}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{6\,{x}^{6}}}-{\frac{B{b}^{5}}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02212, size = 161, normalized size = 1.38 \begin{align*} -\frac{2772 \, B b^{5} x^{6} + 1260 \, A a^{5} + 2310 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + 9900 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 17325 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 7700 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 1386 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x}{13860 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.64076, size = 285, normalized size = 2.44 \begin{align*} -\frac{2772 \, B b^{5} x^{6} + 1260 \, A a^{5} + 2310 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + 9900 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 17325 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 7700 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 1386 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x}{13860 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 13.6743, size = 126, normalized size = 1.08 \begin{align*} - \frac{1260 A a^{5} + 2772 B b^{5} x^{6} + x^{5} \left (2310 A b^{5} + 11550 B a b^{4}\right ) + x^{4} \left (9900 A a b^{4} + 19800 B a^{2} b^{3}\right ) + x^{3} \left (17325 A a^{2} b^{3} + 17325 B a^{3} b^{2}\right ) + x^{2} \left (15400 A a^{3} b^{2} + 7700 B a^{4} b\right ) + x \left (6930 A a^{4} b + 1386 B a^{5}\right )}{13860 x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27275, size = 166, normalized size = 1.42 \begin{align*} -\frac{2772 \, B b^{5} x^{6} + 11550 \, B a b^{4} x^{5} + 2310 \, A b^{5} x^{5} + 19800 \, B a^{2} b^{3} x^{4} + 9900 \, A a b^{4} x^{4} + 17325 \, B a^{3} b^{2} x^{3} + 17325 \, A a^{2} b^{3} x^{3} + 7700 \, B a^{4} b x^{2} + 15400 \, A a^{3} b^{2} x^{2} + 1386 \, B a^{5} x + 6930 \, A a^{4} b x + 1260 \, A a^{5}}{13860 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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