Optimal. Leaf size=62 \[ \frac{10}{7} a^2 b^3 x^7+2 a^3 b^2 x^5+\frac{5}{3} a^4 b x^3+a^5 x+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{11}}{11} \]
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Rubi [A] time = 0.019159, antiderivative size = 62, 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 = {194} \[ \frac{10}{7} a^2 b^3 x^7+2 a^3 b^2 x^5+\frac{5}{3} a^4 b x^3+a^5 x+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{11}}{11} \]
Antiderivative was successfully verified.
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Rule 194
Rubi steps
\begin{align*} \int \left (a+b x^2\right )^5 \, dx &=\int \left (a^5+5 a^4 b x^2+10 a^3 b^2 x^4+10 a^2 b^3 x^6+5 a b^4 x^8+b^5 x^{10}\right ) \, dx\\ &=a^5 x+\frac{5}{3} a^4 b x^3+2 a^3 b^2 x^5+\frac{10}{7} a^2 b^3 x^7+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{11}}{11}\\ \end{align*}
Mathematica [A] time = 0.0009757, size = 62, normalized size = 1. \[ \frac{10}{7} a^2 b^3 x^7+2 a^3 b^2 x^5+\frac{5}{3} a^4 b x^3+a^5 x+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{11}}{11} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 55, normalized size = 0.9 \begin{align*}{a}^{5}x+{\frac{5\,{a}^{4}b{x}^{3}}{3}}+2\,{a}^{3}{b}^{2}{x}^{5}+{\frac{10\,{a}^{2}{b}^{3}{x}^{7}}{7}}+{\frac{5\,a{b}^{4}{x}^{9}}{9}}+{\frac{{b}^{5}{x}^{11}}{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.31468, size = 73, normalized size = 1.18 \begin{align*} \frac{1}{11} \, b^{5} x^{11} + \frac{5}{9} \, a b^{4} x^{9} + \frac{10}{7} \, a^{2} b^{3} x^{7} + 2 \, a^{3} b^{2} x^{5} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.1136, size = 122, normalized size = 1.97 \begin{align*} \frac{1}{11} x^{11} b^{5} + \frac{5}{9} x^{9} b^{4} a + \frac{10}{7} x^{7} b^{3} a^{2} + 2 x^{5} b^{2} a^{3} + \frac{5}{3} x^{3} b a^{4} + x a^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067331, size = 61, normalized size = 0.98 \begin{align*} a^{5} x + \frac{5 a^{4} b x^{3}}{3} + 2 a^{3} b^{2} x^{5} + \frac{10 a^{2} b^{3} x^{7}}{7} + \frac{5 a b^{4} x^{9}}{9} + \frac{b^{5} x^{11}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.29265, size = 73, normalized size = 1.18 \begin{align*} \frac{1}{11} \, b^{5} x^{11} + \frac{5}{9} \, a b^{4} x^{9} + \frac{10}{7} \, a^{2} b^{3} x^{7} + 2 \, a^{3} b^{2} x^{5} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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