Optimal. Leaf size=115 \[ -\frac{5 a^2 b^2 (a B+A b)}{3 x^6}-\frac{a^4 (a B+5 A b)}{8 x^8}-\frac{5 a^3 b (a B+2 A b)}{7 x^7}-\frac{a^5 A}{9 x^9}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{4 x^4}-\frac{b^5 B}{3 x^3} \]
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Rubi [A] time = 0.0544634, antiderivative size = 115, 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} \[ -\frac{5 a^2 b^2 (a B+A b)}{3 x^6}-\frac{a^4 (a B+5 A b)}{8 x^8}-\frac{5 a^3 b (a B+2 A b)}{7 x^7}-\frac{a^5 A}{9 x^9}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{4 x^4}-\frac{b^5 B}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x)^5 (A+B x)}{x^{10}} \, dx &=\int \left (\frac{a^5 A}{x^{10}}+\frac{a^4 (5 A b+a B)}{x^9}+\frac{5 a^3 b (2 A b+a B)}{x^8}+\frac{10 a^2 b^2 (A b+a B)}{x^7}+\frac{5 a b^3 (A b+2 a B)}{x^6}+\frac{b^4 (A b+5 a B)}{x^5}+\frac{b^5 B}{x^4}\right ) \, dx\\ &=-\frac{a^5 A}{9 x^9}-\frac{a^4 (5 A b+a B)}{8 x^8}-\frac{5 a^3 b (2 A b+a B)}{7 x^7}-\frac{5 a^2 b^2 (A b+a B)}{3 x^6}-\frac{a b^3 (A b+2 a B)}{x^5}-\frac{b^4 (A b+5 a B)}{4 x^4}-\frac{b^5 B}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0278264, size = 107, normalized size = 0.93 \[ -\frac{120 a^3 b^2 x^2 (6 A+7 B x)+168 a^2 b^3 x^3 (5 A+6 B x)+45 a^4 b x (7 A+8 B x)+7 a^5 (8 A+9 B x)+126 a b^4 x^4 (4 A+5 B x)+42 b^5 x^5 (3 A+4 B x)}{504 x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 104, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{5}}{9\,{x}^{9}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{8\,{x}^{8}}}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{7\,{x}^{7}}}-{\frac{5\,{b}^{2}{a}^{2} \left ( Ab+Ba \right ) }{3\,{x}^{6}}}-{\frac{a{b}^{3} \left ( Ab+2\,Ba \right ) }{{x}^{5}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{4\,{x}^{4}}}-{\frac{B{b}^{5}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02561, size = 161, normalized size = 1.4 \begin{align*} -\frac{168 \, B b^{5} x^{6} + 56 \, A a^{5} + 126 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + 504 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 840 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 360 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 63 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x}{504 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59878, size = 267, normalized size = 2.32 \begin{align*} -\frac{168 \, B b^{5} x^{6} + 56 \, A a^{5} + 126 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + 504 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 840 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 360 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 63 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x}{504 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 8.58758, size = 126, normalized size = 1.1 \begin{align*} - \frac{56 A a^{5} + 168 B b^{5} x^{6} + x^{5} \left (126 A b^{5} + 630 B a b^{4}\right ) + x^{4} \left (504 A a b^{4} + 1008 B a^{2} b^{3}\right ) + x^{3} \left (840 A a^{2} b^{3} + 840 B a^{3} b^{2}\right ) + x^{2} \left (720 A a^{3} b^{2} + 360 B a^{4} b\right ) + x \left (315 A a^{4} b + 63 B a^{5}\right )}{504 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22439, size = 166, normalized size = 1.44 \begin{align*} -\frac{168 \, B b^{5} x^{6} + 630 \, B a b^{4} x^{5} + 126 \, A b^{5} x^{5} + 1008 \, B a^{2} b^{3} x^{4} + 504 \, A a b^{4} x^{4} + 840 \, B a^{3} b^{2} x^{3} + 840 \, A a^{2} b^{3} x^{3} + 360 \, B a^{4} b x^{2} + 720 \, A a^{3} b^{2} x^{2} + 63 \, B a^{5} x + 315 \, A a^{4} b x + 56 \, A a^{5}}{504 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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