Optimal. Leaf size=113 \[ -\frac {a^5 A}{3 x^3}+a^4 \log (x) (a B+5 A b)+\frac {5}{3} a^3 b x^3 (a B+2 A b)+\frac {5}{3} a^2 b^2 x^6 (a B+A b)+\frac {1}{12} b^4 x^{12} (5 a B+A b)+\frac {5}{9} a b^3 x^9 (2 a B+A b)+\frac {1}{15} b^5 B x^{15} \]
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Rubi [A] time = 0.12, antiderivative size = 113, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {446, 76} \begin {gather*} \frac {5}{3} a^2 b^2 x^6 (a B+A b)+\frac {5}{3} a^3 b x^3 (a B+2 A b)+a^4 \log (x) (a B+5 A b)-\frac {a^5 A}{3 x^3}+\frac {1}{12} b^4 x^{12} (5 a B+A b)+\frac {5}{9} a b^3 x^9 (2 a B+A b)+\frac {1}{15} b^5 B x^{15} \end {gather*}
Antiderivative was successfully verified.
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Rule 76
Rule 446
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^4} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^5 (A+B x)}{x^2} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (5 a^3 b (2 A b+a B)+\frac {a^5 A}{x^2}+\frac {a^4 (5 A b+a B)}{x}+10 a^2 b^2 (A b+a B) x+5 a b^3 (A b+2 a B) x^2+b^4 (A b+5 a B) x^3+b^5 B x^4\right ) \, dx,x,x^3\right )\\ &=-\frac {a^5 A}{3 x^3}+\frac {5}{3} a^3 b (2 A b+a B) x^3+\frac {5}{3} a^2 b^2 (A b+a B) x^6+\frac {5}{9} a b^3 (A b+2 a B) x^9+\frac {1}{12} b^4 (A b+5 a B) x^{12}+\frac {1}{15} b^5 B x^{15}+a^4 (5 A b+a B) \log (x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 115, normalized size = 1.02 \begin {gather*} -\frac {a^5 A}{3 x^3}+\frac {5}{3} a^3 b x^3 (a B+2 A b)+\frac {5}{3} a^2 b^2 x^6 (a B+A b)+\log (x) \left (a^5 B+5 a^4 A b\right )+\frac {1}{12} b^4 x^{12} (5 a B+A b)+\frac {5}{9} a b^3 x^9 (2 a B+A b)+\frac {1}{15} b^5 B x^{15} \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^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.75, size = 123, normalized size = 1.09 \begin {gather*} \frac {12 \, B b^{5} x^{18} + 15 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 100 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 300 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 300 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 60 \, A a^{5} + 180 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3} \log \relax (x)}{180 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 143, normalized size = 1.27 \begin {gather*} \frac {1}{15} \, B b^{5} x^{15} + \frac {5}{12} \, B a b^{4} x^{12} + \frac {1}{12} \, A b^{5} x^{12} + \frac {10}{9} \, B a^{2} b^{3} x^{9} + \frac {5}{9} \, A a b^{4} x^{9} + \frac {5}{3} \, B a^{3} b^{2} x^{6} + \frac {5}{3} \, A a^{2} b^{3} x^{6} + \frac {5}{3} \, B a^{4} b x^{3} + \frac {10}{3} \, A a^{3} b^{2} x^{3} + {\left (B a^{5} + 5 \, A a^{4} b\right )} \log \left ({\left | x \right |}\right ) - \frac {B a^{5} x^{3} + 5 \, A a^{4} b x^{3} + A a^{5}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 123, normalized size = 1.09 \begin {gather*} \frac {B \,b^{5} x^{15}}{15}+\frac {A \,b^{5} x^{12}}{12}+\frac {5 B a \,b^{4} x^{12}}{12}+\frac {5 A a \,b^{4} x^{9}}{9}+\frac {10 B \,a^{2} b^{3} x^{9}}{9}+\frac {5 A \,a^{2} b^{3} x^{6}}{3}+\frac {5 B \,a^{3} b^{2} x^{6}}{3}+\frac {10 A \,a^{3} b^{2} x^{3}}{3}+\frac {5 B \,a^{4} b \,x^{3}}{3}+5 A \,a^{4} b \ln \relax (x )+B \,a^{5} \ln \relax (x )-\frac {A \,a^{5}}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 120, normalized size = 1.06 \begin {gather*} \frac {1}{15} \, B b^{5} x^{15} + \frac {1}{12} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{12} + \frac {5}{9} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{9} + \frac {5}{3} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + \frac {5}{3} \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{3} - \frac {A a^{5}}{3 \, x^{3}} + \frac {1}{3} \, {\left (B a^{5} + 5 \, A a^{4} b\right )} \log \left (x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.35, size = 105, normalized size = 0.93 \begin {gather*} x^{12}\,\left (\frac {A\,b^5}{12}+\frac {5\,B\,a\,b^4}{12}\right )+\ln \relax (x)\,\left (B\,a^5+5\,A\,b\,a^4\right )-\frac {A\,a^5}{3\,x^3}+\frac {B\,b^5\,x^{15}}{15}+\frac {5\,a^2\,b^2\,x^6\,\left (A\,b+B\,a\right )}{3}+\frac {5\,a^3\,b\,x^3\,\left (2\,A\,b+B\,a\right )}{3}+\frac {5\,a\,b^3\,x^9\,\left (A\,b+2\,B\,a\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 133, normalized size = 1.18 \begin {gather*} - \frac {A a^{5}}{3 x^{3}} + \frac {B b^{5} x^{15}}{15} + a^{4} \left (5 A b + B a\right ) \log {\relax (x )} + x^{12} \left (\frac {A b^{5}}{12} + \frac {5 B a b^{4}}{12}\right ) + x^{9} \left (\frac {5 A a b^{4}}{9} + \frac {10 B a^{2} b^{3}}{9}\right ) + x^{6} \left (\frac {5 A a^{2} b^{3}}{3} + \frac {5 B a^{3} b^{2}}{3}\right ) + x^{3} \left (\frac {10 A a^{3} b^{2}}{3} + \frac {5 B a^{4} b}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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