Optimal. Leaf size=55 \[ \frac {1}{4} a^2 A x^4+\frac {1}{6} b x^6 (2 a B+A b)+\frac {1}{5} a x^5 (a B+2 A b)+\frac {1}{7} b^2 B x^7 \]
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Rubi [A] time = 0.03, antiderivative size = 55, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {1}{4} a^2 A x^4+\frac {1}{6} b x^6 (2 a B+A b)+\frac {1}{5} a x^5 (a B+2 A b)+\frac {1}{7} b^2 B x^7 \end {gather*}
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin {align*} \int x^3 (a+b x)^2 (A+B x) \, dx &=\int \left (a^2 A x^3+a (2 A b+a B) x^4+b (A b+2 a B) x^5+b^2 B x^6\right ) \, dx\\ &=\frac {1}{4} a^2 A x^4+\frac {1}{5} a (2 A b+a B) x^5+\frac {1}{6} b (A b+2 a B) x^6+\frac {1}{7} b^2 B x^7\\ \end {align*}
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Mathematica [A] time = 0.01, size = 55, normalized size = 1.00 \begin {gather*} \frac {1}{4} a^2 A x^4+\frac {1}{6} b x^6 (2 a B+A b)+\frac {1}{5} a x^5 (a B+2 A b)+\frac {1}{7} b^2 B x^7 \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^3 (a+b x)^2 (A+B x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.12, size = 53, normalized size = 0.96 \begin {gather*} \frac {1}{7} x^{7} b^{2} B + \frac {1}{3} x^{6} b a B + \frac {1}{6} x^{6} b^{2} A + \frac {1}{5} x^{5} a^{2} B + \frac {2}{5} x^{5} b a A + \frac {1}{4} x^{4} a^{2} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.27, size = 53, normalized size = 0.96 \begin {gather*} \frac {1}{7} \, B b^{2} x^{7} + \frac {1}{3} \, B a b x^{6} + \frac {1}{6} \, A b^{2} x^{6} + \frac {1}{5} \, B a^{2} x^{5} + \frac {2}{5} \, A a b x^{5} + \frac {1}{4} \, A a^{2} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 52, normalized size = 0.95 \begin {gather*} \frac {B \,b^{2} x^{7}}{7}+\frac {A \,a^{2} x^{4}}{4}+\frac {\left (b^{2} A +2 a b B \right ) x^{6}}{6}+\frac {\left (2 a b A +a^{2} B \right ) x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.10, size = 51, normalized size = 0.93 \begin {gather*} \frac {1}{7} \, B b^{2} x^{7} + \frac {1}{4} \, A a^{2} x^{4} + \frac {1}{6} \, {\left (2 \, B a b + A b^{2}\right )} x^{6} + \frac {1}{5} \, {\left (B a^{2} + 2 \, A a b\right )} x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 51, normalized size = 0.93 \begin {gather*} x^5\,\left (\frac {B\,a^2}{5}+\frac {2\,A\,b\,a}{5}\right )+x^6\,\left (\frac {A\,b^2}{6}+\frac {B\,a\,b}{3}\right )+\frac {A\,a^2\,x^4}{4}+\frac {B\,b^2\,x^7}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 54, normalized size = 0.98 \begin {gather*} \frac {A a^{2} x^{4}}{4} + \frac {B b^{2} x^{7}}{7} + x^{6} \left (\frac {A b^{2}}{6} + \frac {B a b}{3}\right ) + x^{5} \left (\frac {2 A a b}{5} + \frac {B a^{2}}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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