Optimal. Leaf size=28 \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0113591, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {12, 194} \[ a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 194
Rubi steps
\begin{align*} \int a \left (e+f x^4\right )^2 \, dx &=a \int \left (e+f x^4\right )^2 \, dx\\ &=a \int \left (e^2+2 e f x^4+f^2 x^8\right ) \, dx\\ &=a e^2 x+\frac{2}{5} a e f x^5+\frac{1}{9} a f^2 x^9\\ \end{align*}
Mathematica [A] time = 0.0017667, size = 27, normalized size = 0.96 \[ a \left (e^2 x+\frac{2}{5} e f x^5+\frac{f^2 x^9}{9}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.04, size = 24, normalized size = 0.9 \begin{align*} a \left ({\frac{{f}^{2}{x}^{9}}{9}}+{\frac{2\,ef{x}^{5}}{5}}+{e}^{2}x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.955677, size = 34, normalized size = 1.21 \begin{align*} \frac{1}{45} \,{\left (5 \, f^{2} x^{9} + 18 \, e f x^{5} + 45 \, e^{2} x\right )} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.05641, size = 55, normalized size = 1.96 \begin{align*} \frac{1}{9} x^{9} f^{2} a + \frac{2}{5} x^{5} f e a + x e^{2} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.059508, size = 27, normalized size = 0.96 \begin{align*} a e^{2} x + \frac{2 a e f x^{5}}{5} + \frac{a f^{2} x^{9}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06919, size = 34, normalized size = 1.21 \begin{align*} \frac{1}{45} \,{\left (5 \, f^{2} x^{9} + 18 \, f x^{5} e + 45 \, x e^{2}\right )} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]