Optimal. Leaf size=28 \[ \frac{1}{5} x^5 (a d+b c)+a c x+\frac{1}{9} b d x^9 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0144161, antiderivative size = 28, 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 = {373} \[ \frac{1}{5} x^5 (a d+b c)+a c x+\frac{1}{9} b d x^9 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 373
Rubi steps
\begin{align*} \int \left (a+b x^4\right ) \left (c+d x^4\right ) \, dx &=\int \left (a c+(b c+a d) x^4+b d x^8\right ) \, dx\\ &=a c x+\frac{1}{5} (b c+a d) x^5+\frac{1}{9} b d x^9\\ \end{align*}
Mathematica [A] time = 0.005435, size = 28, normalized size = 1. \[ \frac{1}{5} x^5 (a d+b c)+a c x+\frac{1}{9} b d x^9 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 25, normalized size = 0.9 \begin{align*} acx+{\frac{ \left ( ad+bc \right ){x}^{5}}{5}}+{\frac{bd{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.948273, size = 32, normalized size = 1.14 \begin{align*} \frac{1}{9} \, b d x^{9} + \frac{1}{5} \,{\left (b c + a d\right )} x^{5} + a c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.946154, size = 66, normalized size = 2.36 \begin{align*} \frac{1}{9} x^{9} d b + \frac{1}{5} x^{5} c b + \frac{1}{5} x^{5} d a + x c a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.057678, size = 26, normalized size = 0.93 \begin{align*} a c x + \frac{b d x^{9}}{9} + x^{5} \left (\frac{a d}{5} + \frac{b c}{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10344, size = 35, normalized size = 1.25 \begin{align*} \frac{1}{9} \, b d x^{9} + \frac{1}{5} \, b c x^{5} + \frac{1}{5} \, a d x^{5} + a c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]