Optimal. Leaf size=117 \[ \frac {1}{5} a^5 A x^5+\frac {1}{6} a^4 x^6 (a B+5 A b)+\frac {5}{7} a^3 b x^7 (a B+2 A b)+\frac {5}{4} a^2 b^2 x^8 (a B+A b)+\frac {1}{10} b^4 x^{10} (5 a B+A b)+\frac {5}{9} a b^3 x^9 (2 a B+A b)+\frac {1}{11} b^5 B x^{11} \]
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Rubi [A] time = 0.07, antiderivative size = 117, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {76} \[ \frac {5}{4} a^2 b^2 x^8 (a B+A b)+\frac {5}{7} a^3 b x^7 (a B+2 A b)+\frac {1}{6} a^4 x^6 (a B+5 A b)+\frac {1}{5} a^5 A x^5+\frac {1}{10} b^4 x^{10} (5 a B+A b)+\frac {5}{9} a b^3 x^9 (2 a B+A b)+\frac {1}{11} b^5 B x^{11} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin {align*} \int x^4 (a+b x)^5 (A+B x) \, dx &=\int \left (a^5 A x^4+a^4 (5 A b+a B) x^5+5 a^3 b (2 A b+a B) x^6+10 a^2 b^2 (A b+a B) x^7+5 a b^3 (A b+2 a B) x^8+b^4 (A b+5 a B) x^9+b^5 B x^{10}\right ) \, dx\\ &=\frac {1}{5} a^5 A x^5+\frac {1}{6} a^4 (5 A b+a B) x^6+\frac {5}{7} a^3 b (2 A b+a B) x^7+\frac {5}{4} a^2 b^2 (A b+a B) x^8+\frac {5}{9} a b^3 (A b+2 a B) x^9+\frac {1}{10} b^4 (A b+5 a B) x^{10}+\frac {1}{11} b^5 B x^{11}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 117, normalized size = 1.00 \[ \frac {1}{5} a^5 A x^5+\frac {1}{6} a^4 x^6 (a B+5 A b)+\frac {5}{7} a^3 b x^7 (a B+2 A b)+\frac {5}{4} a^2 b^2 x^8 (a B+A b)+\frac {1}{10} b^4 x^{10} (5 a B+A b)+\frac {5}{9} a b^3 x^9 (2 a B+A b)+\frac {1}{11} b^5 B x^{11} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 125, normalized size = 1.07 \[ \frac {1}{11} x^{11} b^{5} B + \frac {1}{2} x^{10} b^{4} a B + \frac {1}{10} x^{10} b^{5} A + \frac {10}{9} x^{9} b^{3} a^{2} B + \frac {5}{9} x^{9} b^{4} a A + \frac {5}{4} x^{8} b^{2} a^{3} B + \frac {5}{4} x^{8} b^{3} a^{2} A + \frac {5}{7} x^{7} b a^{4} B + \frac {10}{7} x^{7} b^{2} a^{3} A + \frac {1}{6} x^{6} a^{5} B + \frac {5}{6} x^{6} b a^{4} A + \frac {1}{5} x^{5} a^{5} A \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 125, normalized size = 1.07 \[ \frac {1}{11} \, B b^{5} x^{11} + \frac {1}{2} \, B a b^{4} x^{10} + \frac {1}{10} \, A b^{5} x^{10} + \frac {10}{9} \, B a^{2} b^{3} x^{9} + \frac {5}{9} \, A a b^{4} x^{9} + \frac {5}{4} \, B a^{3} b^{2} x^{8} + \frac {5}{4} \, A a^{2} b^{3} x^{8} + \frac {5}{7} \, B a^{4} b x^{7} + \frac {10}{7} \, A a^{3} b^{2} x^{7} + \frac {1}{6} \, B a^{5} x^{6} + \frac {5}{6} \, A a^{4} b x^{6} + \frac {1}{5} \, A a^{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 124, normalized size = 1.06 \[ \frac {B \,b^{5} x^{11}}{11}+\frac {A \,a^{5} x^{5}}{5}+\frac {\left (b^{5} A +5 a \,b^{4} B \right ) x^{10}}{10}+\frac {\left (5 a \,b^{4} A +10 a^{2} b^{3} B \right ) x^{9}}{9}+\frac {\left (10 a^{2} b^{3} A +10 a^{3} b^{2} B \right ) x^{8}}{8}+\frac {\left (10 a^{3} b^{2} A +5 a^{4} b B \right ) x^{7}}{7}+\frac {\left (5 a^{4} b A +a^{5} B \right ) x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 119, normalized size = 1.02 \[ \frac {1}{11} \, B b^{5} x^{11} + \frac {1}{5} \, A a^{5} x^{5} + \frac {1}{10} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + \frac {5}{9} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{9} + \frac {5}{4} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{8} + \frac {5}{7} \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{7} + \frac {1}{6} \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 107, normalized size = 0.91 \[ x^6\,\left (\frac {B\,a^5}{6}+\frac {5\,A\,b\,a^4}{6}\right )+x^{10}\,\left (\frac {A\,b^5}{10}+\frac {B\,a\,b^4}{2}\right )+\frac {A\,a^5\,x^5}{5}+\frac {B\,b^5\,x^{11}}{11}+\frac {5\,a^2\,b^2\,x^8\,\left (A\,b+B\,a\right )}{4}+\frac {5\,a^3\,b\,x^7\,\left (2\,A\,b+B\,a\right )}{7}+\frac {5\,a\,b^3\,x^9\,\left (A\,b+2\,B\,a\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 136, normalized size = 1.16 \[ \frac {A a^{5} x^{5}}{5} + \frac {B b^{5} x^{11}}{11} + x^{10} \left (\frac {A b^{5}}{10} + \frac {B a b^{4}}{2}\right ) + x^{9} \left (\frac {5 A a b^{4}}{9} + \frac {10 B a^{2} b^{3}}{9}\right ) + x^{8} \left (\frac {5 A a^{2} b^{3}}{4} + \frac {5 B a^{3} b^{2}}{4}\right ) + x^{7} \left (\frac {10 A a^{3} b^{2}}{7} + \frac {5 B a^{4} b}{7}\right ) + x^{6} \left (\frac {5 A a^{4} b}{6} + \frac {B a^{5}}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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