Optimal. Leaf size=117 \[ -\frac {a^5 A}{22 x^{22}}-\frac {a^4 (5 A b+a B)}{19 x^{19}}-\frac {5 a^3 b (2 A b+a B)}{16 x^{16}}-\frac {10 a^2 b^2 (A b+a B)}{13 x^{13}}-\frac {a b^3 (A b+2 a B)}{2 x^{10}}-\frac {b^4 (A b+5 a B)}{7 x^7}-\frac {b^5 B}{4 x^4} \]
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Rubi [A]
time = 0.04, antiderivative size = 117, 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 = {459}
\begin {gather*} -\frac {a^5 A}{22 x^{22}}-\frac {a^4 (a B+5 A b)}{19 x^{19}}-\frac {5 a^3 b (a B+2 A b)}{16 x^{16}}-\frac {10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac {b^4 (5 a B+A b)}{7 x^7}-\frac {a b^3 (2 a B+A b)}{2 x^{10}}-\frac {b^5 B}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 459
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{23}} \, dx &=\int \left (\frac {a^5 A}{x^{23}}+\frac {a^4 (5 A b+a B)}{x^{20}}+\frac {5 a^3 b (2 A b+a B)}{x^{17}}+\frac {10 a^2 b^2 (A b+a B)}{x^{14}}+\frac {5 a b^3 (A b+2 a B)}{x^{11}}+\frac {b^4 (A b+5 a B)}{x^8}+\frac {b^5 B}{x^5}\right ) \, dx\\ &=-\frac {a^5 A}{22 x^{22}}-\frac {a^4 (5 A b+a B)}{19 x^{19}}-\frac {5 a^3 b (2 A b+a B)}{16 x^{16}}-\frac {10 a^2 b^2 (A b+a B)}{13 x^{13}}-\frac {a b^3 (A b+2 a B)}{2 x^{10}}-\frac {b^4 (A b+5 a B)}{7 x^7}-\frac {b^5 B}{4 x^4}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 117, normalized size = 1.00 \begin {gather*} -\frac {a^5 A}{22 x^{22}}-\frac {a^4 (5 A b+a B)}{19 x^{19}}-\frac {5 a^3 b (2 A b+a B)}{16 x^{16}}-\frac {10 a^2 b^2 (A b+a B)}{13 x^{13}}-\frac {a b^3 (A b+2 a B)}{2 x^{10}}-\frac {b^4 (A b+5 a B)}{7 x^7}-\frac {b^5 B}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 104, normalized size = 0.89
method | result | size |
default | \(-\frac {a^{5} A}{22 x^{22}}-\frac {a^{4} \left (5 A b +B a \right )}{19 x^{19}}-\frac {5 a^{3} b \left (2 A b +B a \right )}{16 x^{16}}-\frac {10 a^{2} b^{2} \left (A b +B a \right )}{13 x^{13}}-\frac {a \,b^{3} \left (A b +2 B a \right )}{2 x^{10}}-\frac {b^{4} \left (A b +5 B a \right )}{7 x^{7}}-\frac {b^{5} B}{4 x^{4}}\) | \(104\) |
norman | \(\frac {-\frac {a^{5} A}{22}+\left (-\frac {5}{19} a^{4} b A -\frac {1}{19} a^{5} B \right ) x^{3}+\left (-\frac {5}{8} a^{3} b^{2} A -\frac {5}{16} a^{4} b B \right ) x^{6}+\left (-\frac {10}{13} a^{2} b^{3} A -\frac {10}{13} a^{3} b^{2} B \right ) x^{9}+\left (-\frac {1}{2} a \,b^{4} A -a^{2} b^{3} B \right ) x^{12}+\left (-\frac {1}{7} b^{5} A -\frac {5}{7} a \,b^{4} B \right ) x^{15}-\frac {b^{5} B \,x^{18}}{4}}{x^{22}}\) | \(122\) |
risch | \(\frac {-\frac {a^{5} A}{22}+\left (-\frac {5}{19} a^{4} b A -\frac {1}{19} a^{5} B \right ) x^{3}+\left (-\frac {5}{8} a^{3} b^{2} A -\frac {5}{16} a^{4} b B \right ) x^{6}+\left (-\frac {10}{13} a^{2} b^{3} A -\frac {10}{13} a^{3} b^{2} B \right ) x^{9}+\left (-\frac {1}{2} a \,b^{4} A -a^{2} b^{3} B \right ) x^{12}+\left (-\frac {1}{7} b^{5} A -\frac {5}{7} a \,b^{4} B \right ) x^{15}-\frac {b^{5} B \,x^{18}}{4}}{x^{22}}\) | \(122\) |
gosper | \(-\frac {76076 b^{5} B \,x^{18}+43472 A \,b^{5} x^{15}+217360 B a \,b^{4} x^{15}+152152 a A \,b^{4} x^{12}+304304 B \,a^{2} b^{3} x^{12}+234080 a^{2} A \,b^{3} x^{9}+234080 B \,a^{3} b^{2} x^{9}+190190 a^{3} A \,b^{2} x^{6}+95095 B \,a^{4} b \,x^{6}+80080 a^{4} A b \,x^{3}+16016 B \,a^{5} x^{3}+13832 a^{5} A}{304304 x^{22}}\) | \(128\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 121, normalized size = 1.03 \begin {gather*} -\frac {76076 \, B b^{5} x^{18} + 43472 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 152152 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 234080 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 95095 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 13832 \, A a^{5} + 16016 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{304304 \, x^{22}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.45, size = 121, normalized size = 1.03 \begin {gather*} -\frac {76076 \, B b^{5} x^{18} + 43472 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 152152 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 234080 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 95095 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 13832 \, A a^{5} + 16016 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{304304 \, x^{22}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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Giac [A]
time = 2.06, size = 127, normalized size = 1.09 \begin {gather*} -\frac {76076 \, B b^{5} x^{18} + 217360 \, B a b^{4} x^{15} + 43472 \, A b^{5} x^{15} + 304304 \, B a^{2} b^{3} x^{12} + 152152 \, A a b^{4} x^{12} + 234080 \, B a^{3} b^{2} x^{9} + 234080 \, A a^{2} b^{3} x^{9} + 95095 \, B a^{4} b x^{6} + 190190 \, A a^{3} b^{2} x^{6} + 16016 \, B a^{5} x^{3} + 80080 \, A a^{4} b x^{3} + 13832 \, A a^{5}}{304304 \, x^{22}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 121, normalized size = 1.03 \begin {gather*} -\frac {\frac {A\,a^5}{22}+x^{12}\,\left (B\,a^2\,b^3+\frac {A\,a\,b^4}{2}\right )+x^6\,\left (\frac {5\,B\,a^4\,b}{16}+\frac {5\,A\,a^3\,b^2}{8}\right )+x^3\,\left (\frac {B\,a^5}{19}+\frac {5\,A\,b\,a^4}{19}\right )+x^{15}\,\left (\frac {A\,b^5}{7}+\frac {5\,B\,a\,b^4}{7}\right )+x^9\,\left (\frac {10\,B\,a^3\,b^2}{13}+\frac {10\,A\,a^2\,b^3}{13}\right )+\frac {B\,b^5\,x^{18}}{4}}{x^{22}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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