Optimal. Leaf size=37 \[ \frac {1}{3} a A x^3+\frac {1}{4} a B x^4+\frac {1}{5} A c x^5+\frac {1}{6} B c x^6 \]
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Rubi [A]
time = 0.04, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {780}
\begin {gather*} \frac {1}{3} a A x^3+\frac {1}{4} a B x^4+\frac {1}{5} A c x^5+\frac {1}{6} B c x^6 \end {gather*}
Antiderivative was successfully verified.
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Rule 780
Rubi steps
\begin {align*} \int x^2 (A+B x) \left (a+c x^2\right ) \, dx &=\int \left (a A x^2+a B x^3+A c x^4+B c x^5\right ) \, dx\\ &=\frac {1}{3} a A x^3+\frac {1}{4} a B x^4+\frac {1}{5} A c x^5+\frac {1}{6} B c x^6\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 37, normalized size = 1.00 \begin {gather*} \frac {1}{3} a A x^3+\frac {1}{4} a B x^4+\frac {1}{5} A c x^5+\frac {1}{6} B c x^6 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 30, normalized size = 0.81
method | result | size |
gosper | \(\frac {1}{3} a A \,x^{3}+\frac {1}{4} B a \,x^{4}+\frac {1}{5} A c \,x^{5}+\frac {1}{6} B c \,x^{6}\) | \(30\) |
default | \(\frac {1}{3} a A \,x^{3}+\frac {1}{4} B a \,x^{4}+\frac {1}{5} A c \,x^{5}+\frac {1}{6} B c \,x^{6}\) | \(30\) |
norman | \(\frac {1}{3} a A \,x^{3}+\frac {1}{4} B a \,x^{4}+\frac {1}{5} A c \,x^{5}+\frac {1}{6} B c \,x^{6}\) | \(30\) |
risch | \(\frac {1}{3} a A \,x^{3}+\frac {1}{4} B a \,x^{4}+\frac {1}{5} A c \,x^{5}+\frac {1}{6} B c \,x^{6}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 29, normalized size = 0.78 \begin {gather*} \frac {1}{6} \, B c x^{6} + \frac {1}{5} \, A c x^{5} + \frac {1}{4} \, B a x^{4} + \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 = 2.08, size = 29, normalized size = 0.78 \begin {gather*} \frac {1}{6} \, B c x^{6} + \frac {1}{5} \, A c x^{5} + \frac {1}{4} \, B a x^{4} + \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 = 32, normalized size = 0.86 \begin {gather*} \frac {A a x^{3}}{3} + \frac {A c x^{5}}{5} + \frac {B a x^{4}}{4} + \frac {B c x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.77, size = 29, normalized size = 0.78 \begin {gather*} \frac {1}{6} \, B c x^{6} + \frac {1}{5} \, A c x^{5} + \frac {1}{4} \, B a x^{4} + \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 = 0.04, size = 29, normalized size = 0.78 \begin {gather*} \frac {B\,c\,x^6}{6}+\frac {A\,c\,x^5}{5}+\frac {B\,a\,x^4}{4}+\frac {A\,a\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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