Optimal. Leaf size=110 \[ -\frac {a^5 A}{17 x^{17}}-\frac {a^4 (a B+5 A b)}{14 x^{14}}-\frac {5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac {5 a^2 b^2 (a B+A b)}{4 x^8}-\frac {b^4 (5 a B+A b)}{2 x^2}-\frac {a b^3 (2 a B+A b)}{x^5}+b^5 B x \]
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Rubi [A] time = 0.06, antiderivative size = 110, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {448} \begin {gather*} -\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 \end {gather*}
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*}
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Mathematica [A] time = 0.05, size = 110, normalized size = 1.00 \begin {gather*} -\frac {a^5 A}{17 x^{17}}-\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 {5 a^2 b^2 (a B+A b)}{4 x^8}-\frac {b^4 (5 a B+A b)}{2 x^2}-\frac {a b^3 (2 a B+A b)}{x^5}+b^5 B x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{18}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.67, size = 121, normalized size = 1.10 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 125, normalized size = 1.14 \begin {gather*} 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 101, normalized size = 0.92 \begin {gather*} B \,b^{5} x -\frac {\left (A b +5 B a \right ) b^{4}}{2 x^{2}}-\frac {\left (A b +2 B a \right ) a \,b^{3}}{x^{5}}-\frac {5 \left (A b +B a \right ) a^{2} b^{2}}{4 x^{8}}-\frac {5 \left (2 A b +B a \right ) a^{3} b}{11 x^{11}}-\frac {\left (5 A b +B a \right ) a^{4}}{14 x^{14}}-\frac {A \,a^{5}}{17 x^{17}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 119, normalized size = 1.08 \begin {gather*} 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 119, normalized size = 1.08 \begin {gather*} B\,b^5\,x-\frac {\frac {A\,a^5}{17}+x^{12}\,\left (2\,B\,a^2\,b^3+A\,a\,b^4\right )+x^6\,\left (\frac {5\,B\,a^4\,b}{11}+\frac {10\,A\,a^3\,b^2}{11}\right )+x^3\,\left (\frac {B\,a^5}{14}+\frac {5\,A\,b\,a^4}{14}\right )+x^{15}\,\left (\frac {A\,b^5}{2}+\frac {5\,B\,a\,b^4}{2}\right )+x^9\,\left (\frac {5\,B\,a^3\,b^2}{4}+\frac {5\,A\,a^2\,b^3}{4}\right )}{x^{17}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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