Optimal. Leaf size=47 \[ \frac {1}{5} x^5 (a B+A b)+\frac {1}{4} a A x^4+\frac {1}{6} x^6 (A c+b B)+\frac {1}{7} B c x^7 \]
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Rubi [A] time = 0.06, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {765} \begin {gather*} \frac {1}{5} x^5 (a B+A b)+\frac {1}{4} a A x^4+\frac {1}{6} x^6 (A c+b B)+\frac {1}{7} B c x^7 \end {gather*}
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int x^3 (A+B x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a A x^3+(A b+a B) x^4+(b B+A c) x^5+B c x^6\right ) \, dx\\ &=\frac {1}{4} a A x^4+\frac {1}{5} (A b+a B) x^5+\frac {1}{6} (b B+A c) x^6+\frac {1}{7} B c x^7\\ \end {align*}
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Mathematica [A] time = 0.01, size = 47, normalized size = 1.00 \begin {gather*} \frac {1}{5} x^5 (a B+A b)+\frac {1}{4} a A x^4+\frac {1}{6} x^6 (A c+b B)+\frac {1}{7} B c 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) \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 = 0.34, size = 43, normalized size = 0.91 \begin {gather*} \frac {1}{7} x^{7} c B + \frac {1}{6} x^{6} b B + \frac {1}{6} x^{6} c A + \frac {1}{5} x^{5} a B + \frac {1}{5} x^{5} b A + \frac {1}{4} x^{4} a A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 43, normalized size = 0.91 \begin {gather*} \frac {1}{7} \, B c x^{7} + \frac {1}{6} \, B b x^{6} + \frac {1}{6} \, A c x^{6} + \frac {1}{5} \, B a x^{5} + \frac {1}{5} \, A b x^{5} + \frac {1}{4} \, A a x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 40, normalized size = 0.85 \begin {gather*} \frac {B c \,x^{7}}{7}+\frac {A a \,x^{4}}{4}+\frac {\left (A c +b B \right ) x^{6}}{6}+\frac {\left (A b +B a \right ) x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 39, normalized size = 0.83 \begin {gather*} \frac {1}{7} \, B c x^{7} + \frac {1}{6} \, {\left (B b + A c\right )} x^{6} + \frac {1}{4} \, A a x^{4} + \frac {1}{5} \, {\left (B 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 = 41, normalized size = 0.87 \begin {gather*} \frac {B\,c\,x^7}{7}+\left (\frac {A\,c}{6}+\frac {B\,b}{6}\right )\,x^6+\left (\frac {A\,b}{5}+\frac {B\,a}{5}\right )\,x^5+\frac {A\,a\,x^4}{4} \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^{4}}{4} + \frac {B c x^{7}}{7} + x^{6} \left (\frac {A c}{6} + \frac {B b}{6}\right ) + x^{5} \left (\frac {A b}{5} + \frac {B a}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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