Optimal. Leaf size=14 \[ \frac{(c+d x)^8}{8 d} \]
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Rubi [A] time = 0.0015101, 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} \[ \frac{(c+d x)^8}{8 d} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int (c+d x)^7 \, dx &=\frac{(c+d x)^8}{8 d}\\ \end{align*}
Mathematica [A] time = 0.0015981, size = 14, normalized size = 1. \[ \frac{(c+d x)^8}{8 d} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( dx+c \right ) ^{8}}{8\,d}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.943771, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (d x + c\right )}^{8}}{8 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.97808, size = 159, normalized size = 11.36 \begin{align*} \frac{1}{8} x^{8} d^{7} + x^{7} d^{6} c + \frac{7}{2} x^{6} d^{5} c^{2} + 7 x^{5} d^{4} c^{3} + \frac{35}{4} x^{4} d^{3} c^{4} + 7 x^{3} d^{2} c^{5} + \frac{7}{2} x^{2} d c^{6} + x c^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.070815, size = 83, normalized size = 5.93 \begin{align*} c^{7} x + \frac{7 c^{6} d x^{2}}{2} + 7 c^{5} d^{2} x^{3} + \frac{35 c^{4} d^{3} x^{4}}{4} + 7 c^{3} d^{4} x^{5} + \frac{7 c^{2} d^{5} x^{6}}{2} + c d^{6} x^{7} + \frac{d^{7} x^{8}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04431, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (d x + c\right )}^{8}}{8 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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