Optimal. Leaf size=33 \[ \frac{1}{3} x^3 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{4} B c x^4 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0186484, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {631} \[ \frac{1}{3} x^3 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{4} B c x^4 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 631
Rubi steps
\begin{align*} \int (A+B x) \left (b x+c x^2\right ) \, dx &=\int \left (A b x+(b B+A c) x^2+B c x^3\right ) \, dx\\ &=\frac{1}{2} A b x^2+\frac{1}{3} (b B+A c) x^3+\frac{1}{4} B c x^4\\ \end{align*}
Mathematica [A] time = 0.0046684, size = 29, normalized size = 0.88 \[ \frac{1}{12} x^2 (A (6 b+4 c x)+B x (4 b+3 c x)) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 28, normalized size = 0.9 \begin{align*}{\frac{Ab{x}^{2}}{2}}+{\frac{ \left ( Ac+bB \right ){x}^{3}}{3}}+{\frac{Bc{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.00872, size = 36, normalized size = 1.09 \begin{align*} \frac{1}{4} \, B c x^{4} + \frac{1}{2} \, A b x^{2} + \frac{1}{3} \,{\left (B b + A c\right )} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.65132, size = 74, normalized size = 2.24 \begin{align*} \frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} b B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} b A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.061519, size = 29, normalized size = 0.88 \begin{align*} \frac{A b x^{2}}{2} + \frac{B c x^{4}}{4} + x^{3} \left (\frac{A c}{3} + \frac{B b}{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.2034, size = 39, normalized size = 1.18 \begin{align*} \frac{1}{4} \, B c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, A b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]