Optimal. Leaf size=33 \[ \frac {1}{4} x^4 (A c+b B)+\frac {1}{3} A b x^3+\frac {1}{5} B c x^5 \]
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Rubi [A] time = 0.03, antiderivative size = 33, 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 = {765} \[ \frac {1}{4} x^4 (A c+b B)+\frac {1}{3} A b x^3+\frac {1}{5} B c x^5 \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int x (A+B x) \left (b x+c x^2\right ) \, dx &=\int \left (A b x^2+(b B+A c) x^3+B c x^4\right ) \, dx\\ &=\frac {1}{3} 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 = 0.00, size = 33, normalized size = 1.00 \[ \frac {1}{4} x^4 (A c+b B)+\frac {1}{3} A b x^3+\frac {1}{5} B c x^5 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 29, normalized size = 0.88 \[ \frac {1}{5} x^{5} c B + \frac {1}{4} x^{4} b B + \frac {1}{4} x^{4} c A + \frac {1}{3} x^{3} b A \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 29, normalized size = 0.88 \[ \frac {1}{5} \, B c x^{5} + \frac {1}{4} \, B b x^{4} + \frac {1}{4} \, A c x^{4} + \frac {1}{3} \, A b x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 28, normalized size = 0.85 \[ \frac {B c \,x^{5}}{5}+\frac {A b \,x^{3}}{3}+\frac {\left (A c +b B \right ) x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 27, normalized size = 0.82 \[ \frac {1}{5} \, B c x^{5} + \frac {1}{3} \, A b x^{3} + \frac {1}{4} \, {\left (B b + A c\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.85 \[ \frac {B\,c\,x^5}{5}+\left (\frac {A\,c}{4}+\frac {B\,b}{4}\right )\,x^4+\frac {A\,b\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 29, normalized size = 0.88 \[ \frac {A b x^{3}}{3} + \frac {B c x^{5}}{5} + x^{4} \left (\frac {A c}{4} + \frac {B b}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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