Optimal. Leaf size=14 \[ \frac{(a+b x)^8}{8 b} \]
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Rubi [A] time = 0.0017025, 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} \[ \frac{(a+b x)^8}{8 b} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int (a+b x)^7 \, dx &=\frac{(a+b x)^8}{8 b}\\ \end{align*}
Mathematica [A] time = 0.000834, size = 14, normalized size = 1. \[ \frac{(a+b x)^8}{8 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( bx+a \right ) ^{8}}{8\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06137, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (b x + a\right )}^{8}}{8 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.33431, size = 159, normalized size = 11.36 \begin{align*} \frac{1}{8} x^{8} b^{7} + x^{7} b^{6} a + \frac{7}{2} x^{6} b^{5} a^{2} + 7 x^{5} b^{4} a^{3} + \frac{35}{4} x^{4} b^{3} a^{4} + 7 x^{3} b^{2} a^{5} + \frac{7}{2} x^{2} b a^{6} + x a^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.103633, size = 83, normalized size = 5.93 \begin{align*} a^{7} x + \frac{7 a^{6} b x^{2}}{2} + 7 a^{5} b^{2} x^{3} + \frac{35 a^{4} b^{3} x^{4}}{4} + 7 a^{3} b^{4} x^{5} + \frac{7 a^{2} b^{5} x^{6}}{2} + a b^{6} x^{7} + \frac{b^{7} x^{8}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22762, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (b x + a\right )}^{8}}{8 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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