Optimal. Leaf size=14 \[ -\frac{1}{7 x^7 (b+c x)^7} \]
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Rubi [A] time = 0.002028, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {74} \[ -\frac{1}{7 x^7 (b+c x)^7} \]
Antiderivative was successfully verified.
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Rule 74
Rubi steps
\begin{align*} \int \frac{b+2 c x}{x^8 (b+c x)^8} \, dx &=-\frac{1}{7 x^7 (b+c x)^7}\\ \end{align*}
Mathematica [A] time = 0.0204685, size = 14, normalized size = 1. \[ -\frac{1}{7 x^7 (b+c x)^7} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.02, size = 177, normalized size = 12.6 \begin{align*} 132\,{\frac{{c}^{7}}{{b}^{13} \left ( cx+b \right ) }}+66\,{\frac{{c}^{7}}{{b}^{12} \left ( cx+b \right ) ^{2}}}+30\,{\frac{{c}^{7}}{{b}^{11} \left ( cx+b \right ) ^{3}}}+12\,{\frac{{c}^{7}}{{b}^{10} \left ( cx+b \right ) ^{4}}}+4\,{\frac{{c}^{7}}{{b}^{9} \left ( cx+b \right ) ^{5}}}+{\frac{{c}^{7}}{{b}^{8} \left ( cx+b \right ) ^{6}}}+{\frac{{c}^{7}}{7\,{b}^{7} \left ( cx+b \right ) ^{7}}}-{\frac{1}{7\,{b}^{7}{x}^{7}}}-132\,{\frac{{c}^{6}}{{b}^{13}x}}+66\,{\frac{{c}^{5}}{{b}^{12}{x}^{2}}}-30\,{\frac{{c}^{4}}{{b}^{11}{x}^{3}}}+12\,{\frac{{c}^{3}}{{b}^{10}{x}^{4}}}-4\,{\frac{{c}^{2}}{{b}^{9}{x}^{5}}}+{\frac{c}{{b}^{8}{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.971204, size = 109, normalized size = 7.79 \begin{align*} -\frac{1}{7 \,{\left (c^{7} x^{14} + 7 \, b c^{6} x^{13} + 21 \, b^{2} c^{5} x^{12} + 35 \, b^{3} c^{4} x^{11} + 35 \, b^{4} c^{3} x^{10} + 21 \, b^{5} c^{2} x^{9} + 7 \, b^{6} c x^{8} + b^{7} x^{7}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.951381, size = 171, normalized size = 12.21 \begin{align*} -\frac{1}{7 \,{\left (c^{7} x^{14} + 7 \, b c^{6} x^{13} + 21 \, b^{2} c^{5} x^{12} + 35 \, b^{3} c^{4} x^{11} + 35 \, b^{4} c^{3} x^{10} + 21 \, b^{5} c^{2} x^{9} + 7 \, b^{6} c x^{8} + b^{7} x^{7}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 3.77256, size = 87, normalized size = 6.21 \begin{align*} - \frac{1}{7 b^{7} x^{7} + 49 b^{6} c x^{8} + 147 b^{5} c^{2} x^{9} + 245 b^{4} c^{3} x^{10} + 245 b^{3} c^{4} x^{11} + 147 b^{2} c^{5} x^{12} + 49 b c^{6} x^{13} + 7 c^{7} x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06779, size = 18, normalized size = 1.29 \begin{align*} -\frac{1}{7 \,{\left (c x^{2} + b x\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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