Optimal. Leaf size=91 \[ -\frac {a^5 B}{15 x^{15}}-\frac {5 a^4 b B}{12 x^{12}}-\frac {10 a^3 b^2 B}{9 x^9}-\frac {5 a^2 b^3 B}{3 x^6}-\frac {A \left (a+b x^3\right )^6}{18 a x^{18}}-\frac {5 a b^4 B}{3 x^3}+b^5 B \log (x) \]
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Rubi [A] time = 0.05, antiderivative size = 91, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {446, 78, 43} \[ -\frac {5 a^2 b^3 B}{3 x^6}-\frac {10 a^3 b^2 B}{9 x^9}-\frac {5 a^4 b B}{12 x^{12}}-\frac {a^5 B}{15 x^{15}}-\frac {A \left (a+b x^3\right )^6}{18 a x^{18}}-\frac {5 a b^4 B}{3 x^3}+b^5 B \log (x) \]
Antiderivative was successfully verified.
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Rule 43
Rule 78
Rule 446
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{19}} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^5 (A+B x)}{x^7} \, dx,x,x^3\right )\\ &=-\frac {A \left (a+b x^3\right )^6}{18 a x^{18}}+\frac {1}{3} B \operatorname {Subst}\left (\int \frac {(a+b x)^5}{x^6} \, dx,x,x^3\right )\\ &=-\frac {A \left (a+b x^3\right )^6}{18 a x^{18}}+\frac {1}{3} B \operatorname {Subst}\left (\int \left (\frac {a^5}{x^6}+\frac {5 a^4 b}{x^5}+\frac {10 a^3 b^2}{x^4}+\frac {10 a^2 b^3}{x^3}+\frac {5 a b^4}{x^2}+\frac {b^5}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^5 B}{15 x^{15}}-\frac {5 a^4 b B}{12 x^{12}}-\frac {10 a^3 b^2 B}{9 x^9}-\frac {5 a^2 b^3 B}{3 x^6}-\frac {5 a b^4 B}{3 x^3}-\frac {A \left (a+b x^3\right )^6}{18 a x^{18}}+b^5 B \log (x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 121, normalized size = 1.33 \[ -\frac {2 a^5 \left (5 A+6 B x^3\right )+15 a^4 b x^3 \left (4 A+5 B x^3\right )+50 a^3 b^2 x^6 \left (3 A+4 B x^3\right )+100 a^2 b^3 x^9 \left (2 A+3 B x^3\right )+150 a b^4 x^{12} \left (A+2 B x^3\right )+60 A b^5 x^{15}-180 b^5 B x^{18} \log (x)}{180 x^{18}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.39, size = 123, normalized size = 1.35 \[ \frac {180 \, B b^{5} x^{18} \log \relax (x) - 60 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} - 150 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 200 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 75 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 10 \, A a^{5} - 12 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 136, normalized size = 1.49 \[ B b^{5} \log \left ({\left | x \right |}\right ) - \frac {147 \, B b^{5} x^{18} + 300 \, B a b^{4} x^{15} + 60 \, A b^{5} x^{15} + 300 \, B a^{2} b^{3} x^{12} + 150 \, A a b^{4} x^{12} + 200 \, B a^{3} b^{2} x^{9} + 200 \, A a^{2} b^{3} x^{9} + 75 \, B a^{4} b x^{6} + 150 \, A a^{3} b^{2} x^{6} + 12 \, B a^{5} x^{3} + 60 \, A a^{4} b x^{3} + 10 \, A a^{5}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 124, normalized size = 1.36 \[ B \,b^{5} \ln \relax (x )-\frac {A \,b^{5}}{3 x^{3}}-\frac {5 B a \,b^{4}}{3 x^{3}}-\frac {5 A a \,b^{4}}{6 x^{6}}-\frac {5 B \,a^{2} b^{3}}{3 x^{6}}-\frac {10 A \,a^{2} b^{3}}{9 x^{9}}-\frac {10 B \,a^{3} b^{2}}{9 x^{9}}-\frac {5 A \,a^{3} b^{2}}{6 x^{12}}-\frac {5 B \,a^{4} b}{12 x^{12}}-\frac {A \,a^{4} b}{3 x^{15}}-\frac {B \,a^{5}}{15 x^{15}}-\frac {A \,a^{5}}{18 x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 123, normalized size = 1.35 \[ \frac {1}{3} \, B b^{5} \log \left (x^{3}\right ) - \frac {60 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 150 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 200 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 75 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 10 \, A a^{5} + 12 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 121, normalized size = 1.33 \[ B\,b^5\,\ln \relax (x)-\frac {\frac {A\,a^5}{18}+x^{12}\,\left (\frac {5\,B\,a^2\,b^3}{3}+\frac {5\,A\,a\,b^4}{6}\right )+x^6\,\left (\frac {5\,B\,a^4\,b}{12}+\frac {5\,A\,a^3\,b^2}{6}\right )+x^3\,\left (\frac {B\,a^5}{15}+\frac {A\,b\,a^4}{3}\right )+x^{15}\,\left (\frac {A\,b^5}{3}+\frac {5\,B\,a\,b^4}{3}\right )+x^9\,\left (\frac {10\,B\,a^3\,b^2}{9}+\frac {10\,A\,a^2\,b^3}{9}\right )}{x^{18}} \]
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 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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