Optimal. Leaf size=33 \[ \frac {1}{4} x^4 (a B+A b)+\frac {1}{3} a A x^3+\frac {1}{5} b B x^5 \]
[Out]
________________________________________________________________________________________
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 = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {76} \[ \frac {1}{4} x^4 (a B+A b)+\frac {1}{3} a A x^3+\frac {1}{5} b B x^5 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 76
Rubi steps
\begin {align*} \int x^2 (a+b x) (A+B x) \, dx &=\int \left (a A x^2+(A b+a B) x^3+b B x^4\right ) \, dx\\ &=\frac {1}{3} a A x^3+\frac {1}{4} (A b+a B) x^4+\frac {1}{5} b B x^5\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 33, normalized size = 1.00 \[ \frac {1}{4} x^4 (a B+A b)+\frac {1}{3} a A x^3+\frac {1}{5} b B x^5 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.74, size = 29, normalized size = 0.88 \[ \frac {1}{5} x^{5} b B + \frac {1}{4} x^{4} a B + \frac {1}{4} x^{4} b A + \frac {1}{3} x^{3} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.27, size = 29, normalized size = 0.88 \[ \frac {1}{5} \, B b x^{5} + \frac {1}{4} \, B a x^{4} + \frac {1}{4} \, A b x^{4} + \frac {1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 28, normalized size = 0.85 \[ \frac {B b \,x^{5}}{5}+\frac {A a \,x^{3}}{3}+\frac {\left (A b +B a \right ) x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.04, size = 27, normalized size = 0.82 \[ \frac {1}{5} \, B b x^{5} + \frac {1}{3} \, A a x^{3} + \frac {1}{4} \, {\left (B a + A b\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 28, normalized size = 0.85 \[ \frac {B\,b\,x^5}{5}+\left (\frac {A\,b}{4}+\frac {B\,a}{4}\right )\,x^4+\frac {A\,a\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 29, normalized size = 0.88 \[ \frac {A a x^{3}}{3} + \frac {B b x^{5}}{5} + x^{4} \left (\frac {A b}{4} + \frac {B a}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________