Optimal. Leaf size=75 \[ \frac{1}{8} b^2 x^8 (3 A c+b B)+\frac{1}{7} A b^3 x^7+\frac{1}{10} c^2 x^{10} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{11} B c^3 x^{11} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.081268, antiderivative size = 75, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {765} \[ \frac{1}{8} b^2 x^8 (3 A c+b B)+\frac{1}{7} A b^3 x^7+\frac{1}{10} c^2 x^{10} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{11} B c^3 x^{11} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 765
Rubi steps
\begin{align*} \int x^3 (A+B x) \left (b x+c x^2\right )^3 \, dx &=\int \left (A b^3 x^6+b^2 (b B+3 A c) x^7+3 b c (b B+A c) x^8+c^2 (3 b B+A c) x^9+B c^3 x^{10}\right ) \, dx\\ &=\frac{1}{7} A b^3 x^7+\frac{1}{8} b^2 (b B+3 A c) x^8+\frac{1}{3} b c (b B+A c) x^9+\frac{1}{10} c^2 (3 b B+A c) x^{10}+\frac{1}{11} B c^3 x^{11}\\ \end{align*}
Mathematica [A] time = 0.0132916, size = 75, normalized size = 1. \[ \frac{1}{8} b^2 x^8 (3 A c+b B)+\frac{1}{7} A b^3 x^7+\frac{1}{10} c^2 x^{10} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{11} B c^3 x^{11} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 76, normalized size = 1. \begin{align*}{\frac{B{c}^{3}{x}^{11}}{11}}+{\frac{ \left ( A{c}^{3}+3\,Bb{c}^{2} \right ){x}^{10}}{10}}+{\frac{ \left ( 3\,Ab{c}^{2}+3\,B{b}^{2}c \right ){x}^{9}}{9}}+{\frac{ \left ( 3\,A{b}^{2}c+{b}^{3}B \right ){x}^{8}}{8}}+{\frac{A{b}^{3}{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.10543, size = 99, normalized size = 1.32 \begin{align*} \frac{1}{11} \, B c^{3} x^{11} + \frac{1}{7} \, A b^{3} x^{7} + \frac{1}{10} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{10} + \frac{1}{3} \,{\left (B b^{2} c + A b c^{2}\right )} x^{9} + \frac{1}{8} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.5707, size = 190, normalized size = 2.53 \begin{align*} \frac{1}{11} x^{11} c^{3} B + \frac{3}{10} x^{10} c^{2} b B + \frac{1}{10} x^{10} c^{3} A + \frac{1}{3} x^{9} c b^{2} B + \frac{1}{3} x^{9} c^{2} b A + \frac{1}{8} x^{8} b^{3} B + \frac{3}{8} x^{8} c b^{2} A + \frac{1}{7} x^{7} b^{3} A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.101604, size = 80, normalized size = 1.07 \begin{align*} \frac{A b^{3} x^{7}}{7} + \frac{B c^{3} x^{11}}{11} + x^{10} \left (\frac{A c^{3}}{10} + \frac{3 B b c^{2}}{10}\right ) + x^{9} \left (\frac{A b c^{2}}{3} + \frac{B b^{2} c}{3}\right ) + x^{8} \left (\frac{3 A b^{2} c}{8} + \frac{B b^{3}}{8}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.12685, size = 104, normalized size = 1.39 \begin{align*} \frac{1}{11} \, B c^{3} x^{11} + \frac{3}{10} \, B b c^{2} x^{10} + \frac{1}{10} \, A c^{3} x^{10} + \frac{1}{3} \, B b^{2} c x^{9} + \frac{1}{3} \, A b c^{2} x^{9} + \frac{1}{8} \, B b^{3} x^{8} + \frac{3}{8} \, A b^{2} c x^{8} + \frac{1}{7} \, A b^{3} x^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]