Optimal. Leaf size=112 \[ -\frac {a^5 A}{x}+\frac {1}{2} a^4 x^2 (a B+5 A b)+a^3 b x^5 (a B+2 A b)+\frac {5}{4} a^2 b^2 x^8 (a B+A b)+\frac {1}{14} b^4 x^{14} (5 a B+A b)+\frac {5}{11} a b^3 x^{11} (2 a B+A b)+\frac {1}{17} b^5 B x^{17} \]
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Rubi [A] time = 0.06, antiderivative size = 112, 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}{4} a^2 b^2 x^8 (a B+A b)+a^3 b x^5 (a B+2 A b)+\frac {1}{2} a^4 x^2 (a B+5 A b)-\frac {a^5 A}{x}+\frac {1}{14} b^4 x^{14} (5 a B+A b)+\frac {5}{11} a b^3 x^{11} (2 a B+A b)+\frac {1}{17} b^5 B x^{17} \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^2} \, dx &=\int \left (\frac {a^5 A}{x^2}+a^4 (5 A b+a B) x+5 a^3 b (2 A b+a B) x^4+10 a^2 b^2 (A b+a B) x^7+5 a b^3 (A b+2 a B) x^{10}+b^4 (A b+5 a B) x^{13}+b^5 B x^{16}\right ) \, dx\\ &=-\frac {a^5 A}{x}+\frac {1}{2} a^4 (5 A b+a B) x^2+a^3 b (2 A b+a B) x^5+\frac {5}{4} a^2 b^2 (A b+a B) x^8+\frac {5}{11} a b^3 (A b+2 a B) x^{11}+\frac {1}{14} b^4 (A b+5 a B) x^{14}+\frac {1}{17} b^5 B x^{17}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 112, normalized size = 1.00 \begin {gather*} -\frac {a^5 A}{x}+\frac {1}{2} a^4 x^2 (a B+5 A b)+a^3 b x^5 (a B+2 A b)+\frac {5}{4} a^2 b^2 x^8 (a B+A b)+\frac {1}{14} b^4 x^{14} (5 a B+A b)+\frac {5}{11} a b^3 x^{11} (2 a B+A b)+\frac {1}{17} b^5 B x^{17} \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^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.76, size = 121, normalized size = 1.08 \begin {gather*} \frac {308 \, B b^{5} x^{18} + 374 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 2380 \, {\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} + 5236 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 5236 \, A a^{5} + 2618 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{5236 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 124, normalized size = 1.11 \begin {gather*} \frac {1}{17} \, B b^{5} x^{17} + \frac {5}{14} \, B a b^{4} x^{14} + \frac {1}{14} \, A b^{5} x^{14} + \frac {10}{11} \, B a^{2} b^{3} x^{11} + \frac {5}{11} \, A a b^{4} x^{11} + \frac {5}{4} \, B a^{3} b^{2} x^{8} + \frac {5}{4} \, A a^{2} b^{3} x^{8} + B a^{4} b x^{5} + 2 \, A a^{3} b^{2} x^{5} + \frac {1}{2} \, B a^{5} x^{2} + \frac {5}{2} \, A a^{4} b x^{2} - \frac {A a^{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 125, normalized size = 1.12 \begin {gather*} \frac {B \,b^{5} x^{17}}{17}+\frac {A \,b^{5} x^{14}}{14}+\frac {5 B a \,b^{4} x^{14}}{14}+\frac {5 A a \,b^{4} x^{11}}{11}+\frac {10 B \,a^{2} b^{3} x^{11}}{11}+\frac {5 A \,a^{2} b^{3} x^{8}}{4}+\frac {5 B \,a^{3} b^{2} x^{8}}{4}+2 A \,a^{3} b^{2} x^{5}+B \,a^{4} b \,x^{5}+\frac {5 A \,a^{4} b \,x^{2}}{2}+\frac {B \,a^{5} x^{2}}{2}-\frac {A \,a^{5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 118, normalized size = 1.05 \begin {gather*} \frac {1}{17} \, B b^{5} x^{17} + \frac {1}{14} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{14} + \frac {5}{11} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{11} + \frac {5}{4} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{8} + {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{5} - \frac {A a^{5}}{x} + \frac {1}{2} \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 106, normalized size = 0.95 \begin {gather*} x^2\,\left (\frac {B\,a^5}{2}+\frac {5\,A\,b\,a^4}{2}\right )+x^{14}\,\left (\frac {A\,b^5}{14}+\frac {5\,B\,a\,b^4}{14}\right )-\frac {A\,a^5}{x}+\frac {B\,b^5\,x^{17}}{17}+\frac {5\,a^2\,b^2\,x^8\,\left (A\,b+B\,a\right )}{4}+a^3\,b\,x^5\,\left (2\,A\,b+B\,a\right )+\frac {5\,a\,b^3\,x^{11}\,\left (A\,b+2\,B\,a\right )}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 129, normalized size = 1.15 \begin {gather*} - \frac {A a^{5}}{x} + \frac {B b^{5} x^{17}}{17} + x^{14} \left (\frac {A b^{5}}{14} + \frac {5 B a b^{4}}{14}\right ) + x^{11} \left (\frac {5 A a b^{4}}{11} + \frac {10 B a^{2} b^{3}}{11}\right ) + x^{8} \left (\frac {5 A a^{2} b^{3}}{4} + \frac {5 B a^{3} b^{2}}{4}\right ) + x^{5} \left (2 A a^{3} b^{2} + B a^{4} b\right ) + x^{2} \left (\frac {5 A a^{4} b}{2} + \frac {B a^{5}}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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