Optimal. Leaf size=25 \[ a^2 x+\frac {2}{5} a c x^5+\frac {c^2 x^9}{9} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, 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} \begin {gather*} a^2 x+\frac {2}{5} a c x^5+\frac {c^2 x^9}{9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 194
Rubi steps
\begin {align*} \int \left (a+c x^4\right )^2 \, dx &=\int \left (a^2+2 a c x^4+c^2 x^8\right ) \, dx\\ &=a^2 x+\frac {2}{5} a c x^5+\frac {c^2 x^9}{9}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} a^2 x+\frac {2}{5} a c x^5+\frac {c^2 x^9}{9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a+c x^4\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.37, size = 21, normalized size = 0.84 \begin {gather*} \frac {1}{9} x^{9} c^{2} + \frac {2}{5} x^{5} c a + x a^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 21, normalized size = 0.84 \begin {gather*} \frac {1}{9} \, c^{2} x^{9} + \frac {2}{5} \, a c x^{5} + a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 22, normalized size = 0.88 \begin {gather*} \frac {1}{9} c^{2} x^{9}+\frac {2}{5} a c \,x^{5}+a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.00, size = 21, normalized size = 0.84 \begin {gather*} \frac {1}{9} \, c^{2} x^{9} + \frac {2}{5} \, a c x^{5} + a^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 21, normalized size = 0.84 \begin {gather*} a^2\,x+\frac {2\,a\,c\,x^5}{5}+\frac {c^2\,x^9}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 22, normalized size = 0.88 \begin {gather*} a^{2} x + \frac {2 a c x^{5}}{5} + \frac {c^{2} x^{9}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________