Optimal. Leaf size=14 \[ -\frac{1}{6 b (a+b x)^6} \]
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Rubi [A] time = 0.0017102, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ -\frac{1}{6 b (a+b x)^6} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int \frac{1}{(a+b x)^7} \, dx &=-\frac{1}{6 b (a+b x)^6}\\ \end{align*}
Mathematica [A] time = 0.0044064, size = 14, normalized size = 1. \[ -\frac{1}{6 b (a+b x)^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \begin{align*} -{\frac{1}{6\,b \left ( bx+a \right ) ^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06624, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{6 \,{\left (b x + a\right )}^{6} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.54331, size = 139, normalized size = 9.93 \begin{align*} -\frac{1}{6 \,{\left (b^{7} x^{6} + 6 \, a b^{6} x^{5} + 15 \, a^{2} b^{5} x^{4} + 20 \, a^{3} b^{4} x^{3} + 15 \, a^{4} b^{3} x^{2} + 6 \, a^{5} b^{2} x + a^{6} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.806741, size = 73, normalized size = 5.21 \begin{align*} - \frac{1}{6 a^{6} b + 36 a^{5} b^{2} x + 90 a^{4} b^{3} x^{2} + 120 a^{3} b^{4} x^{3} + 90 a^{2} b^{5} x^{4} + 36 a b^{6} x^{5} + 6 b^{7} x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19839, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{6 \,{\left (b x + a\right )}^{6} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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