Integrand size = 3, antiderivative size = 7 \[ \int x^3 \, dx=\frac {x^4}{4} \]
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Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {30} \[ \int x^3 \, dx=\frac {x^4}{4} \]
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Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {x^4}{4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int x^3 \, dx=\frac {x^4}{4} \]
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Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86
method | result | size |
gosper | \(\frac {x^{4}}{4}\) | \(6\) |
default | \(\frac {x^{4}}{4}\) | \(6\) |
norman | \(\frac {x^{4}}{4}\) | \(6\) |
risch | \(\frac {x^{4}}{4}\) | \(6\) |
parallelrisch | \(\frac {x^{4}}{4}\) | \(6\) |
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none
Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int x^3 \, dx=\frac {1}{4} \, x^{4} \]
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Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.43 \[ \int x^3 \, dx=\frac {x^{4}}{4} \]
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none
Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int x^3 \, dx=\frac {1}{4} \, x^{4} \]
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none
Time = 0.29 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int x^3 \, dx=\frac {1}{4} \, x^{4} \]
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Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int x^3 \, dx=\frac {x^4}{4} \]
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