Optimal. Leaf size=99 \[ -\frac {a^4 A}{9 x^9}-\frac {a^3 (4 A b+a B)}{8 x^8}-\frac {2 a^2 b (3 A b+2 a B)}{7 x^7}-\frac {a b^2 (2 A b+3 a B)}{3 x^6}-\frac {b^3 (A b+4 a B)}{5 x^5}-\frac {b^4 B}{4 x^4} \]
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Rubi [A]
time = 0.03, antiderivative size = 99, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {27, 77}
\begin {gather*} -\frac {a^4 A}{9 x^9}-\frac {a^3 (a B+4 A b)}{8 x^8}-\frac {2 a^2 b (2 a B+3 A b)}{7 x^7}-\frac {b^3 (4 a B+A b)}{5 x^5}-\frac {a b^2 (3 a B+2 A b)}{3 x^6}-\frac {b^4 B}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 77
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^2}{x^{10}} \, dx &=\int \frac {(a+b x)^4 (A+B x)}{x^{10}} \, dx\\ &=\int \left (\frac {a^4 A}{x^{10}}+\frac {a^3 (4 A b+a B)}{x^9}+\frac {2 a^2 b (3 A b+2 a B)}{x^8}+\frac {2 a b^2 (2 A b+3 a B)}{x^7}+\frac {b^3 (A b+4 a B)}{x^6}+\frac {b^4 B}{x^5}\right ) \, dx\\ &=-\frac {a^4 A}{9 x^9}-\frac {a^3 (4 A b+a B)}{8 x^8}-\frac {2 a^2 b (3 A b+2 a B)}{7 x^7}-\frac {a b^2 (2 A b+3 a B)}{3 x^6}-\frac {b^3 (A b+4 a B)}{5 x^5}-\frac {b^4 B}{4 x^4}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 88, normalized size = 0.89 \begin {gather*} -\frac {126 b^4 x^4 (4 A+5 B x)+336 a b^3 x^3 (5 A+6 B x)+360 a^2 b^2 x^2 (6 A+7 B x)+180 a^3 b x (7 A+8 B x)+35 a^4 (8 A+9 B x)}{2520 x^9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.77, size = 88, normalized size = 0.89
method | result | size |
default | \(-\frac {a^{4} A}{9 x^{9}}-\frac {a^{3} \left (4 A b +B a \right )}{8 x^{8}}-\frac {2 a^{2} b \left (3 A b +2 B a \right )}{7 x^{7}}-\frac {a \,b^{2} \left (2 A b +3 B a \right )}{3 x^{6}}-\frac {b^{3} \left (A b +4 B a \right )}{5 x^{5}}-\frac {b^{4} B}{4 x^{4}}\) | \(88\) |
norman | \(\frac {-\frac {B \,b^{4} x^{5}}{4}+\left (-\frac {1}{5} A \,b^{4}-\frac {4}{5} B a \,b^{3}\right ) x^{4}+\left (-\frac {2}{3} A a \,b^{3}-B \,a^{2} b^{2}\right ) x^{3}+\left (-\frac {6}{7} a^{2} A \,b^{2}-\frac {4}{7} B \,a^{3} b \right ) x^{2}+\left (-\frac {1}{2} A \,a^{3} b -\frac {1}{8} B \,a^{4}\right ) x -\frac {a^{4} A}{9}}{x^{9}}\) | \(97\) |
risch | \(\frac {-\frac {B \,b^{4} x^{5}}{4}+\left (-\frac {1}{5} A \,b^{4}-\frac {4}{5} B a \,b^{3}\right ) x^{4}+\left (-\frac {2}{3} A a \,b^{3}-B \,a^{2} b^{2}\right ) x^{3}+\left (-\frac {6}{7} a^{2} A \,b^{2}-\frac {4}{7} B \,a^{3} b \right ) x^{2}+\left (-\frac {1}{2} A \,a^{3} b -\frac {1}{8} B \,a^{4}\right ) x -\frac {a^{4} A}{9}}{x^{9}}\) | \(97\) |
gosper | \(-\frac {630 B \,b^{4} x^{5}+504 A \,b^{4} x^{4}+2016 x^{4} B a \,b^{3}+1680 a A \,b^{3} x^{3}+2520 x^{3} B \,a^{2} b^{2}+2160 a^{2} A \,b^{2} x^{2}+1440 x^{2} B \,a^{3} b +1260 A \,a^{3} b x +315 B \,a^{4} x +280 a^{4} A}{2520 x^{9}}\) | \(100\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 99, normalized size = 1.00 \begin {gather*} -\frac {630 \, B b^{4} x^{5} + 280 \, A a^{4} + 504 \, {\left (4 \, B a b^{3} + A b^{4}\right )} x^{4} + 840 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} + 720 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 315 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} x}{2520 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.62, size = 99, normalized size = 1.00 \begin {gather*} -\frac {630 \, B b^{4} x^{5} + 280 \, A a^{4} + 504 \, {\left (4 \, B a b^{3} + A b^{4}\right )} x^{4} + 840 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} + 720 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 315 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} x}{2520 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 4.27, size = 107, normalized size = 1.08 \begin {gather*} \frac {- 280 A a^{4} - 630 B b^{4} x^{5} + x^{4} \left (- 504 A b^{4} - 2016 B a b^{3}\right ) + x^{3} \left (- 1680 A a b^{3} - 2520 B a^{2} b^{2}\right ) + x^{2} \left (- 2160 A a^{2} b^{2} - 1440 B a^{3} b\right ) + x \left (- 1260 A a^{3} b - 315 B a^{4}\right )}{2520 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.97, size = 99, normalized size = 1.00 \begin {gather*} -\frac {630 \, B b^{4} x^{5} + 2016 \, B a b^{3} x^{4} + 504 \, A b^{4} x^{4} + 2520 \, B a^{2} b^{2} x^{3} + 1680 \, A a b^{3} x^{3} + 1440 \, B a^{3} b x^{2} + 2160 \, A a^{2} b^{2} x^{2} + 315 \, B a^{4} x + 1260 \, A a^{3} b x + 280 \, A a^{4}}{2520 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 96, normalized size = 0.97 \begin {gather*} -\frac {x\,\left (\frac {B\,a^4}{8}+\frac {A\,b\,a^3}{2}\right )+\frac {A\,a^4}{9}+x^3\,\left (B\,a^2\,b^2+\frac {2\,A\,a\,b^3}{3}\right )+x^2\,\left (\frac {4\,B\,a^3\,b}{7}+\frac {6\,A\,a^2\,b^2}{7}\right )+x^4\,\left (\frac {A\,b^4}{5}+\frac {4\,B\,a\,b^3}{5}\right )+\frac {B\,b^4\,x^5}{4}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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