Optimal. Leaf size=33 \[ \frac {1}{3} a A x^3+\frac {1}{6} (A b+a B) x^6+\frac {1}{9} b B x^9 \]
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Rubi [A]
time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {455, 45}
\begin {gather*} \frac {1}{6} x^6 (a B+A b)+\frac {1}{3} a A x^3+\frac {1}{9} b B x^9 \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 455
Rubi steps
\begin {align*} \int x^2 \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\frac {1}{3} \text {Subst}\left (\int (a+b x) (A+B x) \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (a A+(A b+a B) x+b B x^2\right ) \, dx,x,x^3\right )\\ &=\frac {1}{3} a A x^3+\frac {1}{6} (A b+a B) x^6+\frac {1}{9} b B x^9\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 33, normalized size = 1.00 \begin {gather*} \frac {1}{3} a A x^3+\frac {1}{6} (A b+a B) x^6+\frac {1}{9} b B x^9 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 28, normalized size = 0.85
method | result | size |
default | \(\frac {a A \,x^{3}}{3}+\frac {\left (A b +B a \right ) x^{6}}{6}+\frac {b B \,x^{9}}{9}\) | \(28\) |
norman | \(\frac {b B \,x^{9}}{9}+\left (\frac {A b}{6}+\frac {B a}{6}\right ) x^{6}+\frac {a A \,x^{3}}{3}\) | \(29\) |
gosper | \(\frac {1}{9} b B \,x^{9}+\frac {1}{6} x^{6} A b +\frac {1}{6} x^{6} B a +\frac {1}{3} a A \,x^{3}\) | \(30\) |
risch | \(\frac {1}{9} b B \,x^{9}+\frac {1}{6} x^{6} A b +\frac {1}{6} x^{6} B a +\frac {1}{3} a A \,x^{3}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{9} \, B b x^{9} + \frac {1}{6} \, {\left (B a + A b\right )} x^{6} + \frac {1}{3} \, A a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.23, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{9} \, B b x^{9} + \frac {1}{6} \, {\left (B a + A b\right )} x^{6} + \frac {1}{3} \, A a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 29, normalized size = 0.88 \begin {gather*} \frac {A a x^{3}}{3} + \frac {B b x^{9}}{9} + x^{6} \left (\frac {A b}{6} + \frac {B a}{6}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.64, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{9} \, B b x^{9} + \frac {1}{6} \, B a x^{6} + \frac {1}{6} \, A b x^{6} + \frac {1}{3} \, A a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.20, size = 28, normalized size = 0.85 \begin {gather*} \frac {B\,b\,x^9}{9}+\left (\frac {A\,b}{6}+\frac {B\,a}{6}\right )\,x^6+\frac {A\,a\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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