Integrand size = 13, antiderivative size = 17 \[ \int x \left (b x^2+c x^4\right ) \, dx=\frac {b x^4}{4}+\frac {c x^6}{6} \]
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Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14} \[ \int x \left (b x^2+c x^4\right ) \, dx=\frac {b x^4}{4}+\frac {c x^6}{6} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (b x^3+c x^5\right ) \, dx \\ & = \frac {b x^4}{4}+\frac {c x^6}{6} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int x \left (b x^2+c x^4\right ) \, dx=\frac {b x^4}{4}+\frac {c x^6}{6} \]
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Time = 0.03 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82
method | result | size |
default | \(\frac {1}{4} b \,x^{4}+\frac {1}{6} c \,x^{6}\) | \(14\) |
norman | \(\frac {1}{4} b \,x^{4}+\frac {1}{6} c \,x^{6}\) | \(14\) |
risch | \(\frac {1}{4} b \,x^{4}+\frac {1}{6} c \,x^{6}\) | \(14\) |
parallelrisch | \(\frac {1}{4} b \,x^{4}+\frac {1}{6} c \,x^{6}\) | \(14\) |
gosper | \(\frac {x^{4} \left (2 c \,x^{2}+3 b \right )}{12}\) | \(16\) |
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none
Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int x \left (b x^2+c x^4\right ) \, dx=\frac {1}{6} \, c x^{6} + \frac {1}{4} \, b x^{4} \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71 \[ \int x \left (b x^2+c x^4\right ) \, dx=\frac {b x^{4}}{4} + \frac {c x^{6}}{6} \]
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none
Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int x \left (b x^2+c x^4\right ) \, dx=\frac {1}{6} \, c x^{6} + \frac {1}{4} \, b x^{4} \]
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none
Time = 0.31 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int x \left (b x^2+c x^4\right ) \, dx=\frac {1}{6} \, c x^{6} + \frac {1}{4} \, b x^{4} \]
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Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int x \left (b x^2+c x^4\right ) \, dx=\frac {c\,x^6}{6}+\frac {b\,x^4}{4} \]
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