Integrand size = 12, antiderivative size = 18 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=-3 x-x^2+\left (x+x^2\right )^2+\log (3) \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^4+2 x^3-3 x \]
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Rubi steps \begin{align*} \text {integral}& = -3 x+2 x^3+x^4 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=-3 x+2 x^3+x^4 \]
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Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72
method | result | size |
gosper | \(x^{4}+2 x^{3}-3 x\) | \(13\) |
default | \(x^{4}+2 x^{3}-3 x\) | \(13\) |
norman | \(x^{4}+2 x^{3}-3 x\) | \(13\) |
risch | \(x^{4}+2 x^{3}-3 x\) | \(13\) |
parallelrisch | \(x^{4}+2 x^{3}-3 x\) | \(13\) |
parts | \(x^{4}+2 x^{3}-3 x\) | \(13\) |
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none
Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^{4} + 2 \, x^{3} - 3 \, x \]
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Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.56 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^{4} + 2 x^{3} - 3 x \]
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none
Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^{4} + 2 \, x^{3} - 3 \, x \]
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none
Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x^{4} + 2 \, x^{3} - 3 \, x \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-3+6 x^2+4 x^3\right ) \, dx=x\,\left (x^3+2\,x^2-3\right ) \]
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