Integrand size = 25, antiderivative size = 32 \[ \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx=3 a b x+\frac {3 b^2 x^2}{2}+b c x^3+\frac {c^2 x^4}{4} \]
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Time = 0.00 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx=3 a b x+\frac {3 b^2 x^2}{2}+b c x^3+\frac {c^2 x^4}{4} \]
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Rubi steps \begin{align*} \text {integral}& = 3 a b x+\frac {3 b^2 x^2}{2}+b c x^3+\frac {c^2 x^4}{4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx=3 a b x+\frac {3 b^2 x^2}{2}+b c x^3+\frac {c^2 x^4}{4} \]
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Time = 0.02 (sec) , antiderivative size = 29, normalized size of antiderivative = 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 | \(3 a b x +\frac {3}{2} b^{2} x^{2}+b c \,x^{3}+\frac {1}{4} c^{2} x^{4}\) | \(29\) |
parallelrisch | \(3 a b x +\frac {3}{2} b^{2} x^{2}+b c \,x^{3}+\frac {1}{4} c^{2} x^{4}\) | \(29\) |
parts | \(3 a b x +\frac {3}{2} b^{2} x^{2}+b c \,x^{3}+\frac {1}{4} c^{2} x^{4}\) | \(29\) |
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Time = 0.25 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.88 \[ \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx=\frac {1}{4} \, c^{2} x^{4} + b c x^{3} + \frac {3}{2} \, b^{2} x^{2} + 3 \, a b x \]
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Time = 0.02 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.97 \[ \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx=3 a b x + \frac {3 b^{2} x^{2}}{2} + b c x^{3} + \frac {c^{2} x^{4}}{4} \]
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Time = 0.20 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.88 \[ \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx=\frac {1}{4} \, c^{2} x^{4} + b c x^{3} + \frac {3}{2} \, b^{2} x^{2} + 3 \, a b x \]
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Time = 0.28 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.88 \[ \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx=\frac {1}{4} \, c^{2} x^{4} + b c x^{3} + \frac {3}{2} \, b^{2} x^{2} + 3 \, a b x \]
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Time = 0.02 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.88 \[ \int \left (3 a b+3 b^2 x+3 b c x^2+c^2 x^3\right ) \, dx=\frac {3\,b^2\,x^2}{2}+b\,c\,x^3+3\,a\,b\,x+\frac {c^2\,x^4}{4} \]
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