Optimal. Leaf size=65 \[ \frac {1}{4} x^4 (a C+A b)+\frac {1}{2} a A x^2+\frac {1}{5} x^5 (a D+b B)+\frac {1}{3} a B x^3+\frac {1}{6} b C x^6+\frac {1}{7} b D x^7 \]
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Rubi [A] time = 0.06, antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {1802} \[ \frac {1}{4} x^4 (a C+A b)+\frac {1}{2} a A x^2+\frac {1}{5} x^5 (a D+b B)+\frac {1}{3} a B x^3+\frac {1}{6} b C x^6+\frac {1}{7} b D x^7 \]
Antiderivative was successfully verified.
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Rule 1802
Rubi steps
\begin {align*} \int x \left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right ) \, dx &=\int \left (a A x+a B x^2+(A b+a C) x^3+(b B+a D) x^4+b C x^5+b D x^6\right ) \, dx\\ &=\frac {1}{2} a A x^2+\frac {1}{3} a B x^3+\frac {1}{4} (A b+a C) x^4+\frac {1}{5} (b B+a D) x^5+\frac {1}{6} b C x^6+\frac {1}{7} b D x^7\\ \end {align*}
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Mathematica [A] time = 0.01, size = 65, normalized size = 1.00 \[ \frac {1}{4} x^4 (a C+A b)+\frac {1}{2} a A x^2+\frac {1}{5} x^5 (a D+b B)+\frac {1}{3} a B x^3+\frac {1}{6} b C x^6+\frac {1}{7} b D x^7 \]
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 = 0.32, size = 57, normalized size = 0.88 \[ \frac {1}{7} \, D b x^{7} + \frac {1}{6} \, C b x^{6} + \frac {1}{5} \, D a x^{5} + \frac {1}{5} \, B b x^{5} + \frac {1}{4} \, C a x^{4} + \frac {1}{4} \, A b x^{4} + \frac {1}{3} \, B a x^{3} + \frac {1}{2} \, A a x^{2} \]
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 \[ \frac {D b \,x^{7}}{7}+\frac {C b \,x^{6}}{6}+\frac {B a \,x^{3}}{3}+\frac {\left (b B +a D\right ) x^{5}}{5}+\frac {A a \,x^{2}}{2}+\frac {\left (A b +a C \right ) x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 53, normalized size = 0.82 \[ \frac {1}{7} \, D b x^{7} + \frac {1}{6} \, C b x^{6} + \frac {1}{5} \, {\left (D a + B b\right )} x^{5} + \frac {1}{3} \, B a x^{3} + \frac {1}{4} \, {\left (C a + A b\right )} x^{4} + \frac {1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.19, size = 57, normalized size = 0.88 \[ \frac {a\,x^5\,D}{5}+\frac {b\,x^7\,D}{7}+\frac {A\,a\,x^2}{2}+\frac {B\,a\,x^3}{3}+\frac {A\,b\,x^4}{4}+\frac {C\,a\,x^4}{4}+\frac {B\,b\,x^5}{5}+\frac {C\,b\,x^6}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 60, normalized size = 0.92 \[ \frac {A a x^{2}}{2} + \frac {B a x^{3}}{3} + \frac {C b x^{6}}{6} + \frac {D b x^{7}}{7} + x^{5} \left (\frac {B b}{5} + \frac {D a}{5}\right ) + x^{4} \left (\frac {A b}{4} + \frac {C a}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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