Optimal. Leaf size=17 \[ -\frac{1}{2 b c^8 (a+b x)^2} \]
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Rubi [A] time = 0.0038258, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {21, 32} \[ -\frac{1}{2 b c^8 (a+b x)^2} \]
Antiderivative was successfully verified.
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Rule 21
Rule 32
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{(a c+b c x)^8} \, dx &=\frac{\int \frac{1}{(a+b x)^3} \, dx}{c^8}\\ &=-\frac{1}{2 b c^8 (a+b x)^2}\\ \end{align*}
Mathematica [A] time = 0.0041017, size = 17, normalized size = 1. \[ -\frac{1}{2 b c^8 (a+b x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 16, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,b{c}^{8} \left ( bx+a \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.0553, size = 45, normalized size = 2.65 \begin{align*} -\frac{1}{2 \,{\left (b^{3} c^{8} x^{2} + 2 \, a b^{2} c^{8} x + a^{2} b c^{8}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.45614, size = 65, normalized size = 3.82 \begin{align*} -\frac{1}{2 \,{\left (b^{3} c^{8} x^{2} + 2 \, a b^{2} c^{8} x + a^{2} b c^{8}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.385585, size = 36, normalized size = 2.12 \begin{align*} - \frac{1}{2 a^{2} b c^{8} + 4 a b^{2} c^{8} x + 2 b^{3} c^{8} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04775, size = 20, normalized size = 1.18 \begin{align*} -\frac{1}{2 \,{\left (b x + a\right )}^{2} b c^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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