Optimal. Leaf size=14 \[ \frac{(a+b x)^{11}}{11 b} \]
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Rubi [A] time = 0.0015093, 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} \[ \frac{(a+b x)^{11}}{11 b} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int (a+b x)^{10} \, dx &=\frac{(a+b x)^{11}}{11 b}\\ \end{align*}
Mathematica [A] time = 0.0015456, size = 14, normalized size = 1. \[ \frac{(a+b x)^{11}}{11 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( bx+a \right ) ^{11}}{11\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01827, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (b x + a\right )}^{11}}{11 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.64011, size = 230, normalized size = 16.43 \begin{align*} \frac{1}{11} x^{11} b^{10} + x^{10} b^{9} a + 5 x^{9} b^{8} a^{2} + 15 x^{8} b^{7} a^{3} + 30 x^{7} b^{6} a^{4} + 42 x^{6} b^{5} a^{5} + 42 x^{5} b^{4} a^{6} + 30 x^{4} b^{3} a^{7} + 15 x^{3} b^{2} a^{8} + 5 x^{2} b a^{9} + x a^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.093853, size = 114, normalized size = 8.14 \begin{align*} a^{10} x + 5 a^{9} b x^{2} + 15 a^{8} b^{2} x^{3} + 30 a^{7} b^{3} x^{4} + 42 a^{6} b^{4} x^{5} + 42 a^{5} b^{5} x^{6} + 30 a^{4} b^{6} x^{7} + 15 a^{3} b^{7} x^{8} + 5 a^{2} b^{8} x^{9} + a b^{9} x^{10} + \frac{b^{10} x^{11}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19818, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (b x + a\right )}^{11}}{11 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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