Optimal. Leaf size=115 \[ -\frac {a^5 A}{16 x^{16}}-\frac {a^4 (a B+5 A b)}{13 x^{13}}-\frac {a^3 b (a B+2 A b)}{2 x^{10}}-\frac {10 a^2 b^2 (a B+A b)}{7 x^7}-\frac {b^4 (5 a B+A b)}{x}-\frac {5 a b^3 (2 a B+A b)}{4 x^4}+\frac {1}{2} b^5 B x^2 \]
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Rubi [A] time = 0.06, antiderivative size = 115, 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} \[ -\frac {10 a^2 b^2 (a B+A b)}{7 x^7}-\frac {a^4 (a B+5 A b)}{13 x^{13}}-\frac {a^3 b (a B+2 A b)}{2 x^{10}}-\frac {a^5 A}{16 x^{16}}-\frac {5 a b^3 (2 a B+A b)}{4 x^4}-\frac {b^4 (5 a B+A b)}{x}+\frac {1}{2} b^5 B x^2 \]
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^{17}} \, dx &=\int \left (\frac {a^5 A}{x^{17}}+\frac {a^4 (5 A b+a B)}{x^{14}}+\frac {5 a^3 b (2 A b+a B)}{x^{11}}+\frac {10 a^2 b^2 (A b+a B)}{x^8}+\frac {5 a b^3 (A b+2 a B)}{x^5}+\frac {b^4 (A b+5 a B)}{x^2}+b^5 B x\right ) \, dx\\ &=-\frac {a^5 A}{16 x^{16}}-\frac {a^4 (5 A b+a B)}{13 x^{13}}-\frac {a^3 b (2 A b+a B)}{2 x^{10}}-\frac {10 a^2 b^2 (A b+a B)}{7 x^7}-\frac {5 a b^3 (A b+2 a B)}{4 x^4}-\frac {b^4 (A b+5 a B)}{x}+\frac {1}{2} b^5 B x^2\\ \end {align*}
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Mathematica [A] time = 0.03, size = 118, normalized size = 1.03 \[ -\frac {7 a^5 \left (13 A+16 B x^3\right )+56 a^4 b x^3 \left (10 A+13 B x^3\right )+208 a^3 b^2 x^6 \left (7 A+10 B x^3\right )+520 a^2 b^3 x^9 \left (4 A+7 B x^3\right )+1820 a b^4 x^{12} \left (A+4 B x^3\right )-728 b^5 x^{15} \left (B x^3-2 A\right )}{1456 x^{16}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.36, size = 121, normalized size = 1.05 \[ \frac {728 \, B b^{5} x^{18} - 1456 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} - 1820 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 2080 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 728 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 91 \, A a^{5} - 112 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{1456 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 128, normalized size = 1.11 \[ \frac {1}{2} \, B b^{5} x^{2} - \frac {7280 \, B a b^{4} x^{15} + 1456 \, A b^{5} x^{15} + 3640 \, B a^{2} b^{3} x^{12} + 1820 \, A a b^{4} x^{12} + 2080 \, B a^{3} b^{2} x^{9} + 2080 \, A a^{2} b^{3} x^{9} + 728 \, B a^{4} b x^{6} + 1456 \, A a^{3} b^{2} x^{6} + 112 \, B a^{5} x^{3} + 560 \, A a^{4} b x^{3} + 91 \, A a^{5}}{1456 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 104, normalized size = 0.90 \[ \frac {B \,b^{5} x^{2}}{2}-\frac {\left (A b +5 B a \right ) b^{4}}{x}-\frac {5 \left (A b +2 B a \right ) a \,b^{3}}{4 x^{4}}-\frac {10 \left (A b +B a \right ) a^{2} b^{2}}{7 x^{7}}-\frac {\left (2 A b +B a \right ) a^{3} b}{2 x^{10}}-\frac {\left (5 A b +B a \right ) a^{4}}{13 x^{13}}-\frac {A \,a^{5}}{16 x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 122, normalized size = 1.06 \[ \frac {1}{2} \, B b^{5} x^{2} - \frac {1456 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 1820 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 2080 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 728 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 91 \, A a^{5} + 112 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{1456 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.36, size = 121, normalized size = 1.05 \[ \frac {B\,b^5\,x^2}{2}-\frac {\frac {A\,a^5}{16}+x^6\,\left (\frac {B\,a^4\,b}{2}+A\,a^3\,b^2\right )+x^{12}\,\left (\frac {5\,B\,a^2\,b^3}{2}+\frac {5\,A\,a\,b^4}{4}\right )+x^3\,\left (\frac {B\,a^5}{13}+\frac {5\,A\,b\,a^4}{13}\right )+x^{15}\,\left (A\,b^5+5\,B\,a\,b^4\right )+x^9\,\left (\frac {10\,B\,a^3\,b^2}{7}+\frac {10\,A\,a^2\,b^3}{7}\right )}{x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 66.09, size = 134, normalized size = 1.17 \[ \frac {B b^{5} x^{2}}{2} + \frac {- 91 A a^{5} + x^{15} \left (- 1456 A b^{5} - 7280 B a b^{4}\right ) + x^{12} \left (- 1820 A a b^{4} - 3640 B a^{2} b^{3}\right ) + x^{9} \left (- 2080 A a^{2} b^{3} - 2080 B a^{3} b^{2}\right ) + x^{6} \left (- 1456 A a^{3} b^{2} - 728 B a^{4} b\right ) + x^{3} \left (- 560 A a^{4} b - 112 B a^{5}\right )}{1456 x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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