Integrand size = 3, antiderivative size = 7 \[ \int \frac {1}{x^4} \, dx=-\frac {1}{3 x^3} \]
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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} \[ \int \frac {1}{x^4} \, dx=-\frac {1}{3 x^3} \]
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Rule 30
Rubi steps \begin{align*} \text {integral}& = -\frac {1}{3 x^3} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^4} \, dx=-\frac {1}{3 x^3} \]
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Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86
method | result | size |
gosper | \(-\frac {1}{3 x^{3}}\) | \(6\) |
default | \(-\frac {1}{3 x^{3}}\) | \(6\) |
norman | \(-\frac {1}{3 x^{3}}\) | \(6\) |
risch | \(-\frac {1}{3 x^{3}}\) | \(6\) |
parallelrisch | \(-\frac {1}{3 x^{3}}\) | \(6\) |
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none
Time = 0.22 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^4} \, dx=-\frac {1}{3 \, x^{3}} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^4} \, dx=- \frac {1}{3 x^{3}} \]
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none
Time = 0.23 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^4} \, dx=-\frac {1}{3 \, x^{3}} \]
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none
Time = 0.31 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^4} \, dx=-\frac {1}{3 \, x^{3}} \]
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Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1}{x^4} \, dx=-\frac {1}{3\,x^3} \]
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