Optimal. Leaf size=33 \[ \frac{1}{5} x^5 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{6} B c x^6 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0358081, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {765} \[ \frac{1}{5} x^5 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{6} B c x^6 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 765
Rubi steps
\begin{align*} \int x^2 (A+B x) \left (b x+c x^2\right ) \, dx &=\int \left (A b x^3+(b B+A c) x^4+B c x^5\right ) \, dx\\ &=\frac{1}{4} A b x^4+\frac{1}{5} (b B+A c) x^5+\frac{1}{6} B c x^6\\ \end{align*}
Mathematica [A] time = 0.0045252, size = 33, normalized size = 1. \[ \frac{1}{5} x^5 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{6} B c x^6 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 28, normalized size = 0.9 \begin{align*}{\frac{Ab{x}^{4}}{4}}+{\frac{ \left ( Ac+bB \right ){x}^{5}}{5}}+{\frac{Bc{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.993827, size = 36, normalized size = 1.09 \begin{align*} \frac{1}{6} \, B c x^{6} + \frac{1}{4} \, A b x^{4} + \frac{1}{5} \,{\left (B b + A c\right )} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.48731, size = 74, normalized size = 2.24 \begin{align*} \frac{1}{6} x^{6} c B + \frac{1}{5} x^{5} b B + \frac{1}{5} x^{5} c A + \frac{1}{4} x^{4} b A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.061333, size = 29, normalized size = 0.88 \begin{align*} \frac{A b x^{4}}{4} + \frac{B c x^{6}}{6} + x^{5} \left (\frac{A c}{5} + \frac{B b}{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.16321, size = 39, normalized size = 1.18 \begin{align*} \frac{1}{6} \, B c x^{6} + \frac{1}{5} \, B b x^{5} + \frac{1}{5} \, A c x^{5} + \frac{1}{4} \, A b x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]