Optimal. Leaf size=14 \[ \frac{(a+b x)^{11}}{11 b} \]
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Rubi [A] time = 0.017942, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 51, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.039, Rules used = {2059, 32} \[ \frac{(a+b x)^{11}}{11 b} \]
Antiderivative was successfully verified.
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Rule 2059
Rule 32
Rubi steps
\begin{align*} \int \left (a^5+5 a^4 b x+10 a^3 b^2 x^2+10 a^2 b^3 x^3+5 a b^4 x^4+b^5 x^5\right )^2 \, dx &=\int (a+b x)^{10} \, dx\\ &=\frac{(a+b x)^{11}}{11 b}\\ \end{align*}
Mathematica [A] time = 0.0014514, size = 14, normalized size = 1. \[ \frac{(a+b x)^{11}}{11 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 109, normalized size = 7.8 \begin{align*}{\frac{{b}^{10}{x}^{11}}{11}}+a{b}^{9}{x}^{10}+5\,{a}^{2}{b}^{8}{x}^{9}+15\,{a}^{3}{b}^{7}{x}^{8}+30\,{a}^{4}{b}^{6}{x}^{7}+42\,{a}^{5}{b}^{5}{x}^{6}+42\,{a}^{6}{b}^{4}{x}^{5}+30\,{a}^{7}{b}^{3}{x}^{4}+15\,{a}^{8}{b}^{2}{x}^{3}+5\,{a}^{9}b{x}^{2}+{a}^{10}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.15947, size = 308, normalized size = 22. \begin{align*} \frac{1}{11} \, b^{10} x^{11} + a b^{9} x^{10} + \frac{25}{9} \, a^{2} b^{8} x^{9} + \frac{100}{7} \, a^{4} b^{6} x^{7} + 20 \, a^{6} b^{4} x^{5} + \frac{25}{3} \, a^{8} b^{2} x^{3} + a^{10} x + \frac{1}{3} \,{\left (b^{5} x^{6} + 6 \, a b^{4} x^{5} + 15 \, a^{2} b^{3} x^{4} + 20 \, a^{3} b^{2} x^{3} + 15 \, a^{4} b x^{2}\right )} a^{5} + \frac{5}{21} \,{\left (6 \, b^{5} x^{7} + 35 \, a b^{4} x^{6} + 84 \, a^{2} b^{3} x^{5} + 105 \, a^{3} b^{2} x^{4}\right )} a^{4} b + \frac{5}{42} \,{\left (21 \, b^{5} x^{8} + 120 \, a b^{4} x^{7} + 280 \, a^{2} b^{3} x^{6}\right )} a^{3} b^{2} + \frac{5}{18} \,{\left (8 \, b^{5} x^{9} + 45 \, a b^{4} x^{8}\right )} a^{2} b^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.53508, 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 = 0.086512, 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 [B] time = 1.10229, size = 146, normalized size = 10.43 \begin{align*} \frac{1}{11} \, b^{10} x^{11} + a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{9} + 15 \, a^{3} b^{7} x^{8} + 30 \, a^{4} b^{6} x^{7} + 42 \, a^{5} b^{5} x^{6} + 42 \, a^{6} b^{4} x^{5} + 30 \, a^{7} b^{3} x^{4} + 15 \, a^{8} b^{2} x^{3} + 5 \, a^{9} b x^{2} + a^{10} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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