Optimal. Leaf size=66 \[ -\frac {A b^3}{7 x^7}-\frac {b^2 (3 A c+b B)}{5 x^5}-\frac {c^2 (A c+3 b B)}{x}-\frac {b c (A c+b B)}{x^3}+B c^3 x \]
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Rubi [A] time = 0.05, antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {1584, 448} \[ -\frac {b^2 (3 A c+b B)}{5 x^5}-\frac {A b^3}{7 x^7}-\frac {c^2 (A c+3 b B)}{x}-\frac {b c (A c+b B)}{x^3}+B c^3 x \]
Antiderivative was successfully verified.
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Rule 448
Rule 1584
Rubi steps
\begin {align*} \int \frac {\left (A+B x^2\right ) \left (b x^2+c x^4\right )^3}{x^{14}} \, dx &=\int \frac {\left (A+B x^2\right ) \left (b+c x^2\right )^3}{x^8} \, dx\\ &=\int \left (B c^3+\frac {A b^3}{x^8}+\frac {b^2 (b B+3 A c)}{x^6}+\frac {3 b c (b B+A c)}{x^4}+\frac {c^2 (3 b B+A c)}{x^2}\right ) \, dx\\ &=-\frac {A b^3}{7 x^7}-\frac {b^2 (b B+3 A c)}{5 x^5}-\frac {b c (b B+A c)}{x^3}-\frac {c^2 (3 b B+A c)}{x}+B c^3 x\\ \end {align*}
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Mathematica [A] time = 0.04, size = 66, normalized size = 1.00 \[ -\frac {A b^3}{7 x^7}-\frac {b^2 (3 A c+b B)}{5 x^5}-\frac {c^2 (A c+3 b B)}{x}-\frac {b c (A c+b B)}{x^3}+B c^3 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 75, normalized size = 1.14 \[ \frac {35 \, B c^{3} x^{8} - 35 \, {\left (3 \, B b c^{2} + A c^{3}\right )} x^{6} - 35 \, {\left (B b^{2} c + A b c^{2}\right )} x^{4} - 5 \, A b^{3} - 7 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} x^{2}}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 77, normalized size = 1.17 \[ B c^{3} x - \frac {105 \, B b c^{2} x^{6} + 35 \, A c^{3} x^{6} + 35 \, B b^{2} c x^{4} + 35 \, A b c^{2} x^{4} + 7 \, B b^{3} x^{2} + 21 \, A b^{2} c x^{2} + 5 \, A b^{3}}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 63, normalized size = 0.95 \[ B \,c^{3} x -\frac {\left (A c +3 b B \right ) c^{2}}{x}-\frac {\left (A c +b B \right ) b c}{x^{3}}-\frac {A \,b^{3}}{7 x^{7}}-\frac {\left (3 A c +b B \right ) b^{2}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 73, normalized size = 1.11 \[ B c^{3} x - \frac {35 \, {\left (3 \, B b c^{2} + A c^{3}\right )} x^{6} + 35 \, {\left (B b^{2} c + A b c^{2}\right )} x^{4} + 5 \, A b^{3} + 7 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} x^{2}}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 71, normalized size = 1.08 \[ B\,c^3\,x-\frac {x^4\,\left (B\,b^2\,c+A\,b\,c^2\right )+\frac {A\,b^3}{7}+x^2\,\left (\frac {B\,b^3}{5}+\frac {3\,A\,c\,b^2}{5}\right )+x^6\,\left (A\,c^3+3\,B\,b\,c^2\right )}{x^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.50, size = 80, normalized size = 1.21 \[ B c^{3} x + \frac {- 5 A b^{3} + x^{6} \left (- 35 A c^{3} - 105 B b c^{2}\right ) + x^{4} \left (- 35 A b c^{2} - 35 B b^{2} c\right ) + x^{2} \left (- 21 A b^{2} c - 7 B b^{3}\right )}{35 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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