Optimal. Leaf size=75 \[ -\frac{a^2 (a B+3 A b)}{6 x^6}-\frac{a^3 A}{7 x^7}-\frac{b^2 (3 a B+A b)}{4 x^4}-\frac{3 a b (a B+A b)}{5 x^5}-\frac{b^3 B}{3 x^3} \]
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Rubi [A] time = 0.0340929, antiderivative size = 75, 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} \[ -\frac{a^2 (a B+3 A b)}{6 x^6}-\frac{a^3 A}{7 x^7}-\frac{b^2 (3 a B+A b)}{4 x^4}-\frac{3 a b (a B+A b)}{5 x^5}-\frac{b^3 B}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x)^3 (A+B x)}{x^8} \, dx &=\int \left (\frac{a^3 A}{x^8}+\frac{a^2 (3 A b+a B)}{x^7}+\frac{3 a b (A b+a B)}{x^6}+\frac{b^2 (A b+3 a B)}{x^5}+\frac{b^3 B}{x^4}\right ) \, dx\\ &=-\frac{a^3 A}{7 x^7}-\frac{a^2 (3 A b+a B)}{6 x^6}-\frac{3 a b (A b+a B)}{5 x^5}-\frac{b^2 (A b+3 a B)}{4 x^4}-\frac{b^3 B}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0194462, size = 69, normalized size = 0.92 \[ -\frac{42 a^2 b x (5 A+6 B x)+10 a^3 (6 A+7 B x)+63 a b^2 x^2 (4 A+5 B x)+35 b^3 x^3 (3 A+4 B x)}{420 x^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 66, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{3}}{7\,{x}^{7}}}-{\frac{{a}^{2} \left ( 3\,Ab+Ba \right ) }{6\,{x}^{6}}}-{\frac{3\,ab \left ( Ab+Ba \right ) }{5\,{x}^{5}}}-{\frac{{b}^{2} \left ( Ab+3\,Ba \right ) }{4\,{x}^{4}}}-{\frac{B{b}^{3}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.992542, size = 99, normalized size = 1.32 \begin{align*} -\frac{140 \, B b^{3} x^{4} + 60 \, A a^{3} + 105 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 252 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 70 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87264, size = 170, normalized size = 2.27 \begin{align*} -\frac{140 \, B b^{3} x^{4} + 60 \, A a^{3} + 105 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 252 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 70 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.51975, size = 78, normalized size = 1.04 \begin{align*} - \frac{60 A a^{3} + 140 B b^{3} x^{4} + x^{3} \left (105 A b^{3} + 315 B a b^{2}\right ) + x^{2} \left (252 A a b^{2} + 252 B a^{2} b\right ) + x \left (210 A a^{2} b + 70 B a^{3}\right )}{420 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21151, size = 101, normalized size = 1.35 \begin{align*} -\frac{140 \, B b^{3} x^{4} + 315 \, B a b^{2} x^{3} + 105 \, A b^{3} x^{3} + 252 \, B a^{2} b x^{2} + 252 \, A a b^{2} x^{2} + 70 \, B a^{3} x + 210 \, A a^{2} b x + 60 \, A a^{3}}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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