Optimal. Leaf size=33 \[ \frac {1}{3} x^3 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{4} b B x^4 \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {76} \begin {gather*} \frac {1}{3} x^3 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{4} b B x^4 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 76
Rubi steps
\begin {align*} \int x (a+b x) (A+B x) \, dx &=\int \left (a A x+(A b+a B) x^2+b B x^3\right ) \, dx\\ &=\frac {1}{2} a A x^2+\frac {1}{3} (A b+a B) x^3+\frac {1}{4} b B x^4\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{12} x^2 (a (6 A+4 B x)+b x (4 A+3 B x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x (a+b x) (A+B x) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.16, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{4} x^{4} b B + \frac {1}{3} x^{3} a B + \frac {1}{3} x^{3} b A + \frac {1}{2} x^{2} a A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.21, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{4} \, B b x^{4} + \frac {1}{3} \, B a x^{3} + \frac {1}{3} \, A b x^{3} + \frac {1}{2} \, A a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 28, normalized size = 0.85 \begin {gather*} \frac {B b \,x^{4}}{4}+\frac {A a \,x^{2}}{2}+\frac {\left (A b +B a \right ) x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.98, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{4} \, B b x^{4} + \frac {1}{2} \, A a x^{2} + \frac {1}{3} \, {\left (B a + A b\right )} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 28, normalized size = 0.85 \begin {gather*} \frac {B\,b\,x^4}{4}+\left (\frac {A\,b}{3}+\frac {B\,a}{3}\right )\,x^3+\frac {A\,a\,x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 29, normalized size = 0.88 \begin {gather*} \frac {A a x^{2}}{2} + \frac {B b x^{4}}{4} + x^{3} \left (\frac {A b}{3} + \frac {B a}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________