Optimal. Leaf size=69 \[ \frac {1}{3} x^3 (a C+A b)+a A x+\frac {1}{2} a B x^2+\frac {1}{5} x^5 (A c+b C)+\frac {1}{4} b B x^4+\frac {1}{6} B c x^6+\frac {1}{7} c C x^7 \]
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Rubi [A] time = 0.04, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1657} \[ \frac {1}{3} x^3 (a C+A b)+a A x+\frac {1}{2} a B x^2+\frac {1}{5} x^5 (A c+b C)+\frac {1}{4} b B x^4+\frac {1}{6} B c x^6+\frac {1}{7} c C x^7 \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin {align*} \int \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right ) \, dx &=\int \left (a A+a B x+(A b+a C) x^2+b B x^3+(A c+b C) x^4+B c x^5+c C x^6\right ) \, dx\\ &=a A x+\frac {1}{2} a B x^2+\frac {1}{3} (A b+a C) x^3+\frac {1}{4} b B x^4+\frac {1}{5} (A c+b C) x^5+\frac {1}{6} B c x^6+\frac {1}{7} c C x^7\\ \end {align*}
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Mathematica [A] time = 0.01, size = 69, normalized size = 1.00 \[ \frac {1}{3} x^3 (a C+A b)+a A x+\frac {1}{2} a B x^2+\frac {1}{5} x^5 (A c+b C)+\frac {1}{4} b B x^4+\frac {1}{6} B c x^6+\frac {1}{7} c C x^7 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 61, normalized size = 0.88 \[ \frac {1}{7} x^{7} c C + \frac {1}{6} x^{6} c B + \frac {1}{5} x^{5} b C + \frac {1}{5} x^{5} c A + \frac {1}{4} x^{4} b B + \frac {1}{3} x^{3} a C + \frac {1}{3} x^{3} b A + \frac {1}{2} x^{2} a B + x a A \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 61, normalized size = 0.88 \[ \frac {1}{7} \, C c x^{7} + \frac {1}{6} \, B c x^{6} + \frac {1}{5} \, C b x^{5} + \frac {1}{5} \, A c x^{5} + \frac {1}{4} \, B b x^{4} + \frac {1}{3} \, C a x^{3} + \frac {1}{3} \, A b x^{3} + \frac {1}{2} \, B a x^{2} + A a x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 58, normalized size = 0.84 \[ \frac {C c \,x^{7}}{7}+\frac {B c \,x^{6}}{6}+\frac {B b \,x^{4}}{4}+\frac {\left (A c +b C \right ) x^{5}}{5}+\frac {B a \,x^{2}}{2}+A a x +\frac {\left (A b +a C \right ) x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 57, normalized size = 0.83 \[ \frac {1}{7} \, C c x^{7} + \frac {1}{6} \, B c x^{6} + \frac {1}{4} \, B b x^{4} + \frac {1}{5} \, {\left (C b + A c\right )} x^{5} + \frac {1}{2} \, B a x^{2} + \frac {1}{3} \, {\left (C a + A b\right )} x^{3} + A a x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 59, normalized size = 0.86 \[ \frac {C\,c\,x^7}{7}+\frac {B\,c\,x^6}{6}+\left (\frac {A\,c}{5}+\frac {C\,b}{5}\right )\,x^5+\frac {B\,b\,x^4}{4}+\left (\frac {A\,b}{3}+\frac {C\,a}{3}\right )\,x^3+\frac {B\,a\,x^2}{2}+A\,a\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 65, normalized size = 0.94 \[ A a x + \frac {B a x^{2}}{2} + \frac {B b x^{4}}{4} + \frac {B c x^{6}}{6} + \frac {C c x^{7}}{7} + x^{5} \left (\frac {A c}{5} + \frac {C b}{5}\right ) + x^{3} \left (\frac {A b}{3} + \frac {C a}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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