Optimal. Leaf size=47 \[ \frac {1}{3} x^3 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{4} x^4 (A c+b B)+\frac {1}{5} B c x^5 \]
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Rubi [A] time = 0.04, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {765} \begin {gather*} \frac {1}{3} x^3 (a B+A b)+\frac {1}{2} a A x^2+\frac {1}{4} x^4 (A c+b B)+\frac {1}{5} B c x^5 \end {gather*}
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int x (A+B x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a A x+(A b+a B) x^2+(b B+A c) x^3+B c x^4\right ) \, dx\\ &=\frac {1}{2} a A x^2+\frac {1}{3} (A b+a B) x^3+\frac {1}{4} (b B+A c) x^4+\frac {1}{5} B c x^5\\ \end {align*}
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Mathematica [A] time = 0.01, size = 41, normalized size = 0.87 \begin {gather*} \frac {1}{60} x^2 \left (20 x (a B+A b)+30 a A+15 x^2 (A c+b B)+12 B c x^3\right ) \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 (A+B x) \left (a+b x+c x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.35, size = 43, normalized size = 0.91 \begin {gather*} \frac {1}{5} x^{5} c B + \frac {1}{4} x^{4} b B + \frac {1}{4} x^{4} c A + \frac {1}{3} x^{3} a B + \frac {1}{3} x^{3} b A + \frac {1}{2} x^{2} a A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 43, normalized size = 0.91 \begin {gather*} \frac {1}{5} \, B c x^{5} + \frac {1}{4} \, B b x^{4} + \frac {1}{4} \, A c x^{4} + \frac {1}{3} \, B a x^{3} + \frac {1}{3} \, A b x^{3} + \frac {1}{2} \, A a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 40, normalized size = 0.85 \begin {gather*} \frac {B c \,x^{5}}{5}+\frac {A a \,x^{2}}{2}+\frac {\left (A c +b B \right ) x^{4}}{4}+\frac {\left (A b +B a \right ) x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 39, normalized size = 0.83 \begin {gather*} \frac {1}{5} \, B c x^{5} + \frac {1}{4} \, {\left (B b + A c\right )} x^{4} + \frac {1}{2} \, A a x^{2} + \frac {1}{3} \, {\left (B a + A b\right )} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 41, normalized size = 0.87 \begin {gather*} \frac {B\,c\,x^5}{5}+\left (\frac {A\,c}{4}+\frac {B\,b}{4}\right )\,x^4+\left (\frac {A\,b}{3}+\frac {B\,a}{3}\right )\,x^3+\frac {A\,a\,x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 42, normalized size = 0.89 \begin {gather*} \frac {A a x^{2}}{2} + \frac {B c x^{5}}{5} + x^{4} \left (\frac {A c}{4} + \frac {B b}{4}\right ) + x^{3} \left (\frac {A b}{3} + \frac {B a}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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