Optimal. Leaf size=47 \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} x^6 (A c+b B)+\frac{1}{7} B c x^7 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0619092, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {765} \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} x^6 (A c+b B)+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 765
Rubi steps
\begin{align*} \int x^3 (A+B x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a A x^3+(A b+a B) x^4+(b B+A c) x^5+B c x^6\right ) \, dx\\ &=\frac{1}{4} a A x^4+\frac{1}{5} (A b+a B) x^5+\frac{1}{6} (b B+A c) x^6+\frac{1}{7} B c x^7\\ \end{align*}
Mathematica [A] time = 0.0107335, size = 47, normalized size = 1. \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} x^6 (A c+b B)+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 40, normalized size = 0.9 \begin{align*}{\frac{aA{x}^{4}}{4}}+{\frac{ \left ( Ab+aB \right ){x}^{5}}{5}}+{\frac{ \left ( Ac+bB \right ){x}^{6}}{6}}+{\frac{Bc{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.09605, size = 53, normalized size = 1.13 \begin{align*} \frac{1}{7} \, B c x^{7} + \frac{1}{6} \,{\left (B b + A c\right )} x^{6} + \frac{1}{4} \, A a x^{4} + \frac{1}{5} \,{\left (B a + A b\right )} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.12063, size = 112, normalized size = 2.38 \begin{align*} \frac{1}{7} x^{7} c B + \frac{1}{6} x^{6} b B + \frac{1}{6} x^{6} c A + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} b A + \frac{1}{4} x^{4} a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.094939, size = 42, normalized size = 0.89 \begin{align*} \frac{A a x^{4}}{4} + \frac{B c x^{7}}{7} + x^{6} \left (\frac{A c}{6} + \frac{B b}{6}\right ) + x^{5} \left (\frac{A b}{5} + \frac{B a}{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.19823, size = 58, normalized size = 1.23 \begin{align*} \frac{1}{7} \, B c x^{7} + \frac{1}{6} \, B b x^{6} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{4} \, A a x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]