Optimal. Leaf size=65 \[ \frac {1}{5} x^5 (a C+A b)+\frac {1}{3} a A x^3+\frac {1}{6} x^6 (a D+b B)+\frac {1}{4} a B x^4+\frac {1}{7} b C x^7+\frac {1}{8} b D x^8 \]
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Rubi [A] time = 0.08, antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {1802} \[ \frac {1}{5} x^5 (a C+A b)+\frac {1}{3} a A x^3+\frac {1}{6} x^6 (a D+b B)+\frac {1}{4} a B x^4+\frac {1}{7} b C x^7+\frac {1}{8} b D x^8 \]
Antiderivative was successfully verified.
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Rule 1802
Rubi steps
\begin {align*} \int x^2 \left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right ) \, dx &=\int \left (a A x^2+a B x^3+(A b+a C) x^4+(b B+a D) x^5+b C x^6+b D x^7\right ) \, dx\\ &=\frac {1}{3} a A x^3+\frac {1}{4} a B x^4+\frac {1}{5} (A b+a C) x^5+\frac {1}{6} (b B+a D) x^6+\frac {1}{7} b C x^7+\frac {1}{8} b D x^8\\ \end {align*}
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Mathematica [A] time = 0.02, size = 65, normalized size = 1.00 \[ \frac {1}{5} x^5 (a C+A b)+\frac {1}{3} a A x^3+\frac {1}{6} x^6 (a D+b B)+\frac {1}{4} a B x^4+\frac {1}{7} b C x^7+\frac {1}{8} b D x^8 \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 57, normalized size = 0.88 \[ \frac {1}{8} \, D b x^{8} + \frac {1}{7} \, C b x^{7} + \frac {1}{6} \, D a x^{6} + \frac {1}{6} \, B b x^{6} + \frac {1}{5} \, C a x^{5} + \frac {1}{5} \, A b x^{5} + \frac {1}{4} \, B a x^{4} + \frac {1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 54, normalized size = 0.83 \[ \frac {D b \,x^{8}}{8}+\frac {C b \,x^{7}}{7}+\frac {B a \,x^{4}}{4}+\frac {\left (b B +a D\right ) x^{6}}{6}+\frac {A a \,x^{3}}{3}+\frac {\left (A b +a C \right ) x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 53, normalized size = 0.82 \[ \frac {1}{8} \, D b x^{8} + \frac {1}{7} \, C b x^{7} + \frac {1}{6} \, {\left (D a + B b\right )} x^{6} + \frac {1}{4} \, B a x^{4} + \frac {1}{5} \, {\left (C a + A b\right )} x^{5} + \frac {1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.18, size = 57, normalized size = 0.88 \[ \frac {a\,x^6\,D}{6}+\frac {b\,x^8\,D}{8}+\frac {A\,a\,x^3}{3}+\frac {B\,a\,x^4}{4}+\frac {A\,b\,x^5}{5}+\frac {C\,a\,x^5}{5}+\frac {B\,b\,x^6}{6}+\frac {C\,b\,x^7}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 60, normalized size = 0.92 \[ \frac {A a x^{3}}{3} + \frac {B a x^{4}}{4} + \frac {C b x^{7}}{7} + \frac {D b x^{8}}{8} + x^{6} \left (\frac {B b}{6} + \frac {D a}{6}\right ) + x^{5} \left (\frac {A b}{5} + \frac {C a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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