Optimal. Leaf size=55 \[ \frac {1}{4} A b^2 x^4+\frac {1}{6} c x^6 (A c+2 b B)+\frac {1}{5} b x^5 (2 A c+b B)+\frac {1}{7} B c^2 x^7 \]
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Rubi [A] time = 0.05, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {765} \begin {gather*} \frac {1}{4} A b^2 x^4+\frac {1}{6} c x^6 (A c+2 b B)+\frac {1}{5} b x^5 (2 A c+b B)+\frac {1}{7} B c^2 x^7 \end {gather*}
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 )^2 \, dx &=\int \left (A b^2 x^3+b (b B+2 A c) x^4+c (2 b B+A c) x^5+B c^2 x^6\right ) \, dx\\ &=\frac {1}{4} A b^2 x^4+\frac {1}{5} b (b B+2 A c) x^5+\frac {1}{6} c (2 b B+A c) x^6+\frac {1}{7} B c^2 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 b^2 x^4+\frac {1}{6} c x^6 (A c+2 b B)+\frac {1}{5} b x^5 (2 A c+b B)+\frac {1}{7} B c^2 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 (A+B x) \left (b x+c x^2\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.34, size = 53, normalized size = 0.96 \begin {gather*} \frac {1}{7} x^{7} c^{2} B + \frac {1}{3} x^{6} c b B + \frac {1}{6} x^{6} c^{2} A + \frac {1}{5} x^{5} b^{2} B + \frac {2}{5} x^{5} c b A + \frac {1}{4} x^{4} b^{2} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 53, normalized size = 0.96 \begin {gather*} \frac {1}{7} \, B c^{2} x^{7} + \frac {1}{3} \, B b c x^{6} + \frac {1}{6} \, A c^{2} x^{6} + \frac {1}{5} \, B b^{2} x^{5} + \frac {2}{5} \, A b c x^{5} + \frac {1}{4} \, A b^{2} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 52, normalized size = 0.95 \begin {gather*} \frac {B \,c^{2} x^{7}}{7}+\frac {A \,b^{2} x^{4}}{4}+\frac {\left (A \,c^{2}+2 b B c \right ) x^{6}}{6}+\frac {\left (2 A b c +b^{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 = 0.84, size = 51, normalized size = 0.93 \begin {gather*} \frac {1}{7} \, B c^{2} x^{7} + \frac {1}{4} \, A b^{2} x^{4} + \frac {1}{6} \, {\left (2 \, B b c + A c^{2}\right )} x^{6} + \frac {1}{5} \, {\left (B b^{2} + 2 \, A b c\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\,b^2}{5}+\frac {2\,A\,c\,b}{5}\right )+x^6\,\left (\frac {A\,c^2}{6}+\frac {B\,b\,c}{3}\right )+\frac {A\,b^2\,x^4}{4}+\frac {B\,c^2\,x^7}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 54, normalized size = 0.98 \begin {gather*} \frac {A b^{2} x^{4}}{4} + \frac {B c^{2} x^{7}}{7} + x^{6} \left (\frac {A c^{2}}{6} + \frac {B b c}{3}\right ) + x^{5} \left (\frac {2 A b c}{5} + \frac {B b^{2}}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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