Optimal. Leaf size=34 \[ \frac {1}{2} x^2 \left (a e^2+c d^2\right )+a d e x+\frac {1}{3} c d e x^3 \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {1}{2} x^2 \left (a e^2+c d^2\right )+a d e x+\frac {1}{3} c d e x^3 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin {align*} \int \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right ) \, dx &=a d e x+\frac {1}{2} \left (c d^2+a e^2\right ) x^2+\frac {1}{3} c d e x^3\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 38, normalized size = 1.12 \begin {gather*} a d e x+\frac {1}{2} a e^2 x^2+\frac {1}{2} c d^2 x^2+\frac {1}{3} c d e x^3 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.35, size = 32, normalized size = 0.94 \begin {gather*} \frac {1}{3} x^{3} e d c + \frac {1}{2} x^{2} d^{2} c + \frac {1}{2} x^{2} e^{2} a + x e d a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 31, normalized size = 0.91 \begin {gather*} \frac {1}{3} \, c d x^{3} e + a d x e + \frac {1}{2} \, {\left (c d^{2} + a e^{2}\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 31, normalized size = 0.91 \begin {gather*} \frac {c d e \,x^{3}}{3}+a d e x +\frac {\left (a \,e^{2}+c \,d^{2}\right ) x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.00, size = 30, normalized size = 0.88 \begin {gather*} \frac {1}{3} \, c d e x^{3} + a d e x + \frac {1}{2} \, {\left (c d^{2} + a e^{2}\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 31, normalized size = 0.91 \begin {gather*} \frac {c\,d\,e\,x^3}{3}+\left (\frac {c\,d^2}{2}+\frac {a\,e^2}{2}\right )\,x^2+a\,d\,e\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 32, normalized size = 0.94 \begin {gather*} a d e x + \frac {c d e x^{3}}{3} + x^{2} \left (\frac {a e^{2}}{2} + \frac {c d^{2}}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________