Optimal. Leaf size=17 \[ a c x+\frac {1}{2} x^2 (b c+d) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ a c x+\frac {1}{2} x^2 (b c+d) \]
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin {align*} \int (a c+(b c+d) x) \, dx &=a c x+\frac {1}{2} (b c+d) x^2\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 22, normalized size = 1.29 \[ a c x+\frac {1}{2} b c x^2+\frac {d x^2}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.53, size = 18, normalized size = 1.06 \[ \frac {1}{2} x^{2} c b + \frac {1}{2} x^{2} d + x c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.39, size = 15, normalized size = 0.88 \[ a c x + \frac {1}{2} \, {\left (b c + d\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 16, normalized size = 0.94 \[ a c x +\frac {\left (b c +d \right ) x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.66, size = 15, normalized size = 0.88 \[ a c x + \frac {1}{2} \, {\left (b c + d\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 17, normalized size = 1.00 \[ \left (\frac {d}{2}+\frac {b\,c}{2}\right )\,x^2+a\,c\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 15, normalized size = 0.88 \[ a c x + x^{2} \left (\frac {b c}{2} + \frac {d}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________