Optimal. Leaf size=108 \[ -\frac {a^5 A}{9 x^9}-\frac {a^4 (a B+5 A b)}{7 x^7}-\frac {a^3 b (a B+2 A b)}{x^5}-\frac {10 a^2 b^2 (a B+A b)}{3 x^3}+b^4 x (5 a B+A b)-\frac {5 a b^3 (2 a B+A b)}{x}+\frac {1}{3} b^5 B x^3 \]
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Rubi [A] time = 0.07, antiderivative size = 108, 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} \begin {gather*} -\frac {10 a^2 b^2 (a B+A b)}{3 x^3}-\frac {a^4 (a B+5 A b)}{7 x^7}-\frac {a^3 b (a B+2 A b)}{x^5}-\frac {a^5 A}{9 x^9}-\frac {5 a b^3 (2 a B+A b)}{x}+b^4 x (5 a B+A b)+\frac {1}{3} b^5 B x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^5 \left (A+B x^2\right )}{x^{10}} \, dx &=\int \left (b^4 (A b+5 a B)+\frac {a^5 A}{x^{10}}+\frac {a^4 (5 A b+a B)}{x^8}+\frac {5 a^3 b (2 A b+a B)}{x^6}+\frac {10 a^2 b^2 (A b+a B)}{x^4}+\frac {5 a b^3 (A b+2 a B)}{x^2}+b^5 B x^2\right ) \, dx\\ &=-\frac {a^5 A}{9 x^9}-\frac {a^4 (5 A b+a B)}{7 x^7}-\frac {a^3 b (2 A b+a B)}{x^5}-\frac {10 a^2 b^2 (A b+a B)}{3 x^3}-\frac {5 a b^3 (A b+2 a B)}{x}+b^4 (A b+5 a B) x+\frac {1}{3} b^5 B x^3\\ \end {align*}
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Mathematica [A] time = 0.03, size = 115, normalized size = 1.06 \begin {gather*} -\frac {a^5 \left (7 A+9 B x^2\right )+9 a^4 b x^2 \left (5 A+7 B x^2\right )+42 a^3 b^2 x^4 \left (3 A+5 B x^2\right )+210 a^2 b^3 x^6 \left (A+3 B x^2\right )+315 a b^4 x^8 \left (A-B x^2\right )-21 b^5 x^{10} \left (3 A+B x^2\right )}{63 x^9} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^2\right )^5 \left (A+B x^2\right )}{x^{10}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.73, size = 121, normalized size = 1.12 \begin {gather*} \frac {21 \, B b^{5} x^{12} + 63 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} - 315 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} - 210 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} - 7 \, A a^{5} - 63 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} - 9 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{63 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 123, normalized size = 1.14 \begin {gather*} \frac {1}{3} \, B b^{5} x^{3} + 5 \, B a b^{4} x + A b^{5} x - \frac {630 \, B a^{2} b^{3} x^{8} + 315 \, A a b^{4} x^{8} + 210 \, B a^{3} b^{2} x^{6} + 210 \, A a^{2} b^{3} x^{6} + 63 \, B a^{4} b x^{4} + 126 \, A a^{3} b^{2} x^{4} + 9 \, B a^{5} x^{2} + 45 \, A a^{4} b x^{2} + 7 \, A a^{5}}{63 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 102, normalized size = 0.94 \begin {gather*} \frac {B \,b^{5} x^{3}}{3}+A \,b^{5} x +5 B a \,b^{4} x -\frac {5 \left (A b +2 B a \right ) a \,b^{3}}{x}-\frac {10 \left (A b +B a \right ) a^{2} b^{2}}{3 x^{3}}-\frac {\left (2 A b +B a \right ) a^{3} b}{x^{5}}-\frac {A \,a^{5}}{9 x^{9}}-\frac {\left (5 A b +B a \right ) a^{4}}{7 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 119, normalized size = 1.10 \begin {gather*} \frac {1}{3} \, B b^{5} x^{3} + {\left (5 \, B a b^{4} + A b^{5}\right )} x - \frac {315 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 210 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 7 \, A a^{5} + 63 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 9 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{63 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 119, normalized size = 1.10 \begin {gather*} x\,\left (A\,b^5+5\,B\,a\,b^4\right )-\frac {\frac {A\,a^5}{9}+x^4\,\left (B\,a^4\,b+2\,A\,a^3\,b^2\right )+x^8\,\left (10\,B\,a^2\,b^3+5\,A\,a\,b^4\right )+x^2\,\left (\frac {B\,a^5}{7}+\frac {5\,A\,b\,a^4}{7}\right )+x^6\,\left (\frac {10\,B\,a^3\,b^2}{3}+\frac {10\,A\,a^2\,b^3}{3}\right )}{x^9}+\frac {B\,b^5\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.09, size = 129, normalized size = 1.19 \begin {gather*} \frac {B b^{5} x^{3}}{3} + x \left (A b^{5} + 5 B a b^{4}\right ) + \frac {- 7 A a^{5} + x^{8} \left (- 315 A a b^{4} - 630 B a^{2} b^{3}\right ) + x^{6} \left (- 210 A a^{2} b^{3} - 210 B a^{3} b^{2}\right ) + x^{4} \left (- 126 A a^{3} b^{2} - 63 B a^{4} b\right ) + x^{2} \left (- 45 A a^{4} b - 9 B a^{5}\right )}{63 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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