Optimal. Leaf size=16 \[ -\frac{1}{21 x^{21} \left (b+c x^3\right )^7} \]
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Rubi [A] time = 0.0232854, 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} \[ -\frac{1}{21 x^{21} \left (b+c x^3\right )^7} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 446
Rule 74
Rubi steps
\begin{align*} \int \frac{b+2 c x^3}{x^{14} \left (b x+c x^4\right )^8} \, dx &=\int \frac{b+2 c x^3}{x^{22} \left (b+c x^3\right )^8} \, dx\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{b+2 c x}{x^8 (b+c x)^8} \, dx,x,x^3\right )\\ &=-\frac{1}{21 x^{21} \left (b+c x^3\right )^7}\\ \end{align*}
Mathematica [A] time = 0.035783, size = 16, normalized size = 1. \[ -\frac{1}{21 x^{21} \left (b+c x^3\right )^7} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.013, size = 197, normalized size = 12.3 \begin{align*} -{\frac{{c}^{8}}{3\,{b}^{13}} \left ( -132\,{\frac{1}{c \left ( c{x}^{3}+b \right ) }}-{\frac{{b}^{5}}{c \left ( c{x}^{3}+b \right ) ^{6}}}-4\,{\frac{{b}^{4}}{c \left ( c{x}^{3}+b \right ) ^{5}}}-12\,{\frac{{b}^{3}}{c \left ( c{x}^{3}+b \right ) ^{4}}}-30\,{\frac{{b}^{2}}{c \left ( c{x}^{3}+b \right ) ^{3}}}-{\frac{{b}^{6}}{7\,c \left ( c{x}^{3}+b \right ) ^{7}}}-66\,{\frac{b}{c \left ( c{x}^{3}+b \right ) ^{2}}} \right ) }-{\frac{1}{21\,{b}^{7}{x}^{21}}}-44\,{\frac{{c}^{6}}{{b}^{13}{x}^{3}}}+22\,{\frac{{c}^{5}}{{b}^{12}{x}^{6}}}-10\,{\frac{{c}^{4}}{{b}^{11}{x}^{9}}}+4\,{\frac{{c}^{3}}{{b}^{10}{x}^{12}}}-{\frac{4\,{c}^{2}}{3\,{b}^{9}{x}^{15}}}+{\frac{c}{3\,{b}^{8}{x}^{18}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.12978, size = 109, normalized size = 6.81 \begin{align*} -\frac{1}{21 \,{\left (c^{7} x^{42} + 7 \, b c^{6} x^{39} + 21 \, b^{2} c^{5} x^{36} + 35 \, b^{3} c^{4} x^{33} + 35 \, b^{4} c^{3} x^{30} + 21 \, b^{5} c^{2} x^{27} + 7 \, b^{6} c x^{24} + b^{7} x^{21}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.31839, size = 177, normalized size = 11.06 \begin{align*} -\frac{1}{21 \,{\left (c^{7} x^{42} + 7 \, b c^{6} x^{39} + 21 \, b^{2} c^{5} x^{36} + 35 \, b^{3} c^{4} x^{33} + 35 \, b^{4} c^{3} x^{30} + 21 \, b^{5} c^{2} x^{27} + 7 \, b^{6} c x^{24} + b^{7} x^{21}\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 = 1.43324, size = 20, normalized size = 1.25 \begin{align*} -\frac{1}{21 \,{\left (c x^{6} + b x^{3}\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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