Optimal. Leaf size=30 \[ \frac{(a+b x)^{12}}{12 b^2}-\frac{a (a+b x)^{11}}{11 b^2} \]
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Rubi [A] time = 0.0082832, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ \frac{(a+b x)^{12}}{12 b^2}-\frac{a (a+b x)^{11}}{11 b^2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x (a+b x)^{10} \, dx &=\int \left (-\frac{a (a+b x)^{10}}{b}+\frac{(a+b x)^{11}}{b}\right ) \, dx\\ &=-\frac{a (a+b x)^{11}}{11 b^2}+\frac{(a+b x)^{12}}{12 b^2}\\ \end{align*}
Mathematica [B] time = 0.002549, size = 128, normalized size = 4.27 \[ \frac{9}{2} a^2 b^8 x^{10}+\frac{40}{3} a^3 b^7 x^9+\frac{105}{4} a^4 b^6 x^8+36 a^5 b^5 x^7+35 a^6 b^4 x^6+24 a^7 b^3 x^5+\frac{45}{4} a^8 b^2 x^4+\frac{10}{3} a^9 b x^3+\frac{a^{10} x^2}{2}+\frac{10}{11} a b^9 x^{11}+\frac{b^{10} x^{12}}{12} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 113, normalized size = 3.8 \begin{align*}{\frac{{b}^{10}{x}^{12}}{12}}+{\frac{10\,a{b}^{9}{x}^{11}}{11}}+{\frac{9\,{a}^{2}{b}^{8}{x}^{10}}{2}}+{\frac{40\,{a}^{3}{b}^{7}{x}^{9}}{3}}+{\frac{105\,{a}^{4}{b}^{6}{x}^{8}}{4}}+36\,{a}^{5}{b}^{5}{x}^{7}+35\,{a}^{6}{b}^{4}{x}^{6}+24\,{a}^{7}{b}^{3}{x}^{5}+{\frac{45\,{a}^{8}{b}^{2}{x}^{4}}{4}}+{\frac{10\,{a}^{9}b{x}^{3}}{3}}+{\frac{{a}^{10}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.02693, size = 151, normalized size = 5.03 \begin{align*} \frac{1}{12} \, b^{10} x^{12} + \frac{10}{11} \, a b^{9} x^{11} + \frac{9}{2} \, a^{2} b^{8} x^{10} + \frac{40}{3} \, a^{3} b^{7} x^{9} + \frac{105}{4} \, a^{4} b^{6} x^{8} + 36 \, a^{5} b^{5} x^{7} + 35 \, a^{6} b^{4} x^{6} + 24 \, a^{7} b^{3} x^{5} + \frac{45}{4} \, a^{8} b^{2} x^{4} + \frac{10}{3} \, a^{9} b x^{3} + \frac{1}{2} \, a^{10} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.42404, size = 263, normalized size = 8.77 \begin{align*} \frac{1}{12} x^{12} b^{10} + \frac{10}{11} x^{11} b^{9} a + \frac{9}{2} x^{10} b^{8} a^{2} + \frac{40}{3} x^{9} b^{7} a^{3} + \frac{105}{4} x^{8} b^{6} a^{4} + 36 x^{7} b^{5} a^{5} + 35 x^{6} b^{4} a^{6} + 24 x^{5} b^{3} a^{7} + \frac{45}{4} x^{4} b^{2} a^{8} + \frac{10}{3} x^{3} b a^{9} + \frac{1}{2} x^{2} a^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.111035, size = 129, normalized size = 4.3 \begin{align*} \frac{a^{10} x^{2}}{2} + \frac{10 a^{9} b x^{3}}{3} + \frac{45 a^{8} b^{2} x^{4}}{4} + 24 a^{7} b^{3} x^{5} + 35 a^{6} b^{4} x^{6} + 36 a^{5} b^{5} x^{7} + \frac{105 a^{4} b^{6} x^{8}}{4} + \frac{40 a^{3} b^{7} x^{9}}{3} + \frac{9 a^{2} b^{8} x^{10}}{2} + \frac{10 a b^{9} x^{11}}{11} + \frac{b^{10} x^{12}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.18686, size = 151, normalized size = 5.03 \begin{align*} \frac{1}{12} \, b^{10} x^{12} + \frac{10}{11} \, a b^{9} x^{11} + \frac{9}{2} \, a^{2} b^{8} x^{10} + \frac{40}{3} \, a^{3} b^{7} x^{9} + \frac{105}{4} \, a^{4} b^{6} x^{8} + 36 \, a^{5} b^{5} x^{7} + 35 \, a^{6} b^{4} x^{6} + 24 \, a^{7} b^{3} x^{5} + \frac{45}{4} \, a^{8} b^{2} x^{4} + \frac{10}{3} \, a^{9} b x^{3} + \frac{1}{2} \, a^{10} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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