Optimal. Leaf size=32 \[ 3 a b x+\frac {3 b^2 x^2}{2}+b c x^3+\frac {c^2 x^4}{4} \]
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Rubi [A]
time = 0.00, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} 3 a b x+\frac {3 b^2 x^2}{2}+b c x^3+\frac {c^2 x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx &=3 a b x+\frac {3 b^2 x^2}{2}+b c x^3+\frac {c^2 x^4}{4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 32, normalized size = 1.00 \begin {gather*} 3 a b x+\frac {3 b^2 x^2}{2}+b c x^3+\frac {c^2 x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 29, normalized size = 0.91
method | result | size |
gosper | \(3 a b x +\frac {3}{2} b^{2} x^{2}+b c \,x^{3}+\frac {1}{4} c^{2} x^{4}\) | \(29\) |
default | \(3 a b x +\frac {3}{2} b^{2} x^{2}+b c \,x^{3}+\frac {1}{4} c^{2} x^{4}\) | \(29\) |
norman | \(3 a b x +\frac {3}{2} b^{2} x^{2}+b c \,x^{3}+\frac {1}{4} c^{2} x^{4}\) | \(29\) |
risch | \(3 a b x +\frac {3}{2} b^{2} x^{2}+b c \,x^{3}+\frac {1}{4} c^{2} x^{4}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 28, normalized size = 0.88 \begin {gather*} \frac {1}{4} \, c^{2} x^{4} + b c x^{3} + \frac {3}{2} \, b^{2} x^{2} + 3 \, a b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 28, normalized size = 0.88 \begin {gather*} \frac {1}{4} \, c^{2} x^{4} + b c x^{3} + \frac {3}{2} \, b^{2} x^{2} + 3 \, a b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 31, normalized size = 0.97 \begin {gather*} 3 a b x + \frac {3 b^{2} x^{2}}{2} + b c x^{3} + \frac {c^{2} x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.95, size = 28, normalized size = 0.88 \begin {gather*} \frac {1}{4} \, c^{2} x^{4} + b c x^{3} + \frac {3}{2} \, b^{2} x^{2} + 3 \, a b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 28, normalized size = 0.88 \begin {gather*} \frac {3\,b^2\,x^2}{2}+b\,c\,x^3+3\,a\,b\,x+\frac {c^2\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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