Optimal. Leaf size=75 \[ \frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{6} b^2 x^6 (3 a B+A b)+\frac{3}{5} a b x^5 (a B+A b)+\frac{1}{7} b^3 B x^7 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0420364, antiderivative size = 75, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {76} \[ \frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{6} b^2 x^6 (3 a B+A b)+\frac{3}{5} a b x^5 (a B+A b)+\frac{1}{7} b^3 B x^7 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 76
Rubi steps
\begin{align*} \int x^2 (a+b x)^3 (A+B x) \, dx &=\int \left (a^3 A x^2+a^2 (3 A b+a B) x^3+3 a b (A b+a B) x^4+b^2 (A b+3 a B) x^5+b^3 B x^6\right ) \, dx\\ &=\frac{1}{3} a^3 A x^3+\frac{1}{4} a^2 (3 A b+a B) x^4+\frac{3}{5} a b (A b+a B) x^5+\frac{1}{6} b^2 (A b+3 a B) x^6+\frac{1}{7} b^3 B x^7\\ \end{align*}
Mathematica [A] time = 0.0090785, size = 75, normalized size = 1. \[ \frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{6} b^2 x^6 (3 a B+A b)+\frac{3}{5} a b x^5 (a B+A b)+\frac{1}{7} b^3 B x^7 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 76, normalized size = 1. \begin{align*}{\frac{{b}^{3}B{x}^{7}}{7}}+{\frac{ \left ({b}^{3}A+3\,a{b}^{2}B \right ){x}^{6}}{6}}+{\frac{ \left ( 3\,a{b}^{2}A+3\,{a}^{2}bB \right ){x}^{5}}{5}}+{\frac{ \left ( 3\,{a}^{2}bA+{a}^{3}B \right ){x}^{4}}{4}}+{\frac{{a}^{3}A{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.09362, size = 99, normalized size = 1.32 \begin{align*} \frac{1}{7} \, B b^{3} x^{7} + \frac{1}{3} \, A a^{3} x^{3} + \frac{1}{6} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{6} + \frac{3}{5} \,{\left (B a^{2} b + A a b^{2}\right )} x^{5} + \frac{1}{4} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.42089, size = 182, normalized size = 2.43 \begin{align*} \frac{1}{7} x^{7} b^{3} B + \frac{1}{2} x^{6} b^{2} a B + \frac{1}{6} x^{6} b^{3} A + \frac{3}{5} x^{5} b a^{2} B + \frac{3}{5} x^{5} b^{2} a A + \frac{1}{4} x^{4} a^{3} B + \frac{3}{4} x^{4} b a^{2} A + \frac{1}{3} x^{3} a^{3} A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.07574, size = 82, normalized size = 1.09 \begin{align*} \frac{A a^{3} x^{3}}{3} + \frac{B b^{3} x^{7}}{7} + x^{6} \left (\frac{A b^{3}}{6} + \frac{B a b^{2}}{2}\right ) + x^{5} \left (\frac{3 A a b^{2}}{5} + \frac{3 B a^{2} b}{5}\right ) + x^{4} \left (\frac{3 A a^{2} b}{4} + \frac{B a^{3}}{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.22999, size = 104, normalized size = 1.39 \begin{align*} \frac{1}{7} \, B b^{3} x^{7} + \frac{1}{2} \, B a b^{2} x^{6} + \frac{1}{6} \, A b^{3} x^{6} + \frac{3}{5} \, B a^{2} b x^{5} + \frac{3}{5} \, A a b^{2} x^{5} + \frac{1}{4} \, B a^{3} x^{4} + \frac{3}{4} \, A a^{2} b x^{4} + \frac{1}{3} \, A a^{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]