Optimal. Leaf size=60 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10} \]
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Rubi [A] time = 0.0624218, antiderivative size = 60, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {1850} \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10} \]
Antiderivative was successfully verified.
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Rule 1850
Rubi steps
\begin{align*} \int (a+b x) \left (e+f x^4\right )^2 \, dx &=\int \left (a e^2+b e^2 x+2 a e f x^4+2 b e f x^5+a f^2 x^8+b f^2 x^9\right ) \, dx\\ &=a e^2 x+\frac{1}{2} b e^2 x^2+\frac{2}{5} a e f x^5+\frac{1}{3} b e f x^6+\frac{1}{9} a f^2 x^9+\frac{1}{10} b f^2 x^{10}\\ \end{align*}
Mathematica [A] time = 0.0019781, size = 60, normalized size = 1. \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9+\frac{1}{2} b e^2 x^2+\frac{1}{3} b e f x^6+\frac{1}{10} b f^2 x^{10} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.039, size = 51, normalized size = 0.9 \begin{align*} a{e}^{2}x+{\frac{b{e}^{2}{x}^{2}}{2}}+{\frac{2\,aef{x}^{5}}{5}}+{\frac{bef{x}^{6}}{3}}+{\frac{a{f}^{2}{x}^{9}}{9}}+{\frac{b{f}^{2}{x}^{10}}{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.981534, size = 68, normalized size = 1.13 \begin{align*} \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{3} \, b e f x^{6} + \frac{2}{5} \, a e f x^{5} + \frac{1}{2} \, b e^{2} x^{2} + a e^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.00017, size = 123, normalized size = 2.05 \begin{align*} \frac{1}{10} x^{10} f^{2} b + \frac{1}{9} x^{9} f^{2} a + \frac{1}{3} x^{6} f e b + \frac{2}{5} x^{5} f e a + \frac{1}{2} x^{2} e^{2} b + x e^{2} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.066282, size = 58, normalized size = 0.97 \begin{align*} a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} + \frac{b e^{2} x^{2}}{2} + \frac{b e f x^{6}}{3} + \frac{b f^{2} x^{10}}{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05481, size = 68, normalized size = 1.13 \begin{align*} \frac{1}{10} \, b f^{2} x^{10} + \frac{1}{9} \, a f^{2} x^{9} + \frac{1}{3} \, b f x^{6} e + \frac{2}{5} \, a f x^{5} e + \frac{1}{2} \, b x^{2} e^{2} + a x e^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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