Optimal. Leaf size=16 \[ -\frac{1}{14 x^{14} \left (b+c x^2\right )^7} \]
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Rubi [A] time = 0.023114, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13, Rules used = {1584, 446, 74} \[ -\frac{1}{14 x^{14} \left (b+c x^2\right )^7} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 446
Rule 74
Rubi steps
\begin{align*} \int \frac{b+2 c x^2}{x^7 \left (b x+c x^3\right )^8} \, dx &=\int \frac{b+2 c x^2}{x^{15} \left (b+c x^2\right )^8} \, dx\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{b+2 c x}{x^8 (b+c x)^8} \, dx,x,x^2\right )\\ &=-\frac{1}{14 x^{14} \left (b+c x^2\right )^7}\\ \end{align*}
Mathematica [A] time = 0.028989, size = 16, normalized size = 1. \[ -\frac{1}{14 x^{14} \left (b+c x^2\right )^7} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.018, size = 197, normalized size = 12.3 \begin{align*} -{\frac{1}{14\,{b}^{7}{x}^{14}}}-66\,{\frac{{c}^{6}}{{b}^{13}{x}^{2}}}+33\,{\frac{{c}^{5}}{{b}^{12}{x}^{4}}}-15\,{\frac{{c}^{4}}{{b}^{11}{x}^{6}}}+6\,{\frac{{c}^{3}}{{b}^{10}{x}^{8}}}-2\,{\frac{{c}^{2}}{{b}^{9}{x}^{10}}}+{\frac{c}{2\,{b}^{8}{x}^{12}}}-{\frac{{c}^{8}}{2\,{b}^{13}} \left ( -{\frac{{b}^{6}}{7\,c \left ( c{x}^{2}+b \right ) ^{7}}}-132\,{\frac{1}{c \left ( c{x}^{2}+b \right ) }}-4\,{\frac{{b}^{4}}{c \left ( c{x}^{2}+b \right ) ^{5}}}-12\,{\frac{{b}^{3}}{c \left ( c{x}^{2}+b \right ) ^{4}}}-30\,{\frac{{b}^{2}}{c \left ( c{x}^{2}+b \right ) ^{3}}}-66\,{\frac{b}{c \left ( c{x}^{2}+b \right ) ^{2}}}-{\frac{{b}^{5}}{c \left ( c{x}^{2}+b \right ) ^{6}}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.10015, size = 109, normalized size = 6.81 \begin{align*} -\frac{1}{14 \,{\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.405, size = 177, normalized size = 11.06 \begin{align*} -\frac{1}{14 \,{\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.3487, size = 20, normalized size = 1.25 \begin{align*} -\frac{1}{14 \,{\left (c x^{4} + b x^{2}\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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