Optimal. Leaf size=110 \[ -\frac{5 a^2 b^2 (a B+A b)}{4 x^8}-\frac{a^4 (a B+5 A b)}{14 x^{14}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{17 x^{17}}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{2 x^2}+b^5 B x \]
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Rubi [A] time = 0.0613283, antiderivative size = 110, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ -\frac{5 a^2 b^2 (a B+A b)}{4 x^8}-\frac{a^4 (a B+5 A b)}{14 x^{14}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{17 x^{17}}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{2 x^2}+b^5 B x \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{18}} \, dx &=\int \left (b^5 B+\frac{a^5 A}{x^{18}}+\frac{a^4 (5 A b+a B)}{x^{15}}+\frac{5 a^3 b (2 A b+a B)}{x^{12}}+\frac{10 a^2 b^2 (A b+a B)}{x^9}+\frac{5 a b^3 (A b+2 a B)}{x^6}+\frac{b^4 (A b+5 a B)}{x^3}\right ) \, dx\\ &=-\frac{a^5 A}{17 x^{17}}-\frac{a^4 (5 A b+a B)}{14 x^{14}}-\frac{5 a^3 b (2 A b+a B)}{11 x^{11}}-\frac{5 a^2 b^2 (A b+a B)}{4 x^8}-\frac{a b^3 (A b+2 a B)}{x^5}-\frac{b^4 (A b+5 a B)}{2 x^2}+b^5 B x\\ \end{align*}
Mathematica [A] time = 0.0432395, size = 110, normalized size = 1. \[ -\frac{5 a^2 b^2 (a B+A b)}{4 x^8}-\frac{a^4 (a B+5 A b)}{14 x^{14}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{17 x^{17}}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{2 x^2}+b^5 B x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 101, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{5}}{17\,{x}^{17}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{14\,{x}^{14}}}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{11\,{x}^{11}}}-{\frac{5\,{a}^{2}{b}^{2} \left ( Ab+Ba \right ) }{4\,{x}^{8}}}-{\frac{a{b}^{3} \left ( Ab+2\,Ba \right ) }{{x}^{5}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{2\,{x}^{2}}}+{b}^{5}Bx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.31328, size = 161, normalized size = 1.46 \begin{align*} B b^{5} x - \frac{2618 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 5236 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 6545 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 2380 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 308 \, A a^{5} + 374 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{5236 \, x^{17}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40694, size = 285, normalized size = 2.59 \begin{align*} \frac{5236 \, B b^{5} x^{18} - 2618 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} - 5236 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 6545 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 2380 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 308 \, A a^{5} - 374 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{5236 \, x^{17}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 125.843, size = 122, normalized size = 1.11 \begin{align*} B b^{5} x - \frac{308 A a^{5} + x^{15} \left (2618 A b^{5} + 13090 B a b^{4}\right ) + x^{12} \left (5236 A a b^{4} + 10472 B a^{2} b^{3}\right ) + x^{9} \left (6545 A a^{2} b^{3} + 6545 B a^{3} b^{2}\right ) + x^{6} \left (4760 A a^{3} b^{2} + 2380 B a^{4} b\right ) + x^{3} \left (1870 A a^{4} b + 374 B a^{5}\right )}{5236 x^{17}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19891, size = 169, normalized size = 1.54 \begin{align*} B b^{5} x - \frac{13090 \, B a b^{4} x^{15} + 2618 \, A b^{5} x^{15} + 10472 \, B a^{2} b^{3} x^{12} + 5236 \, A a b^{4} x^{12} + 6545 \, B a^{3} b^{2} x^{9} + 6545 \, A a^{2} b^{3} x^{9} + 2380 \, B a^{4} b x^{6} + 4760 \, A a^{3} b^{2} x^{6} + 374 \, B a^{5} x^{3} + 1870 \, A a^{4} b x^{3} + 308 \, A a^{5}}{5236 \, x^{17}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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