Integrand size = 17, antiderivative size = 20 \[ \int \frac {1}{x \sqrt [4]{-x^3+x^4}} \, dx=\frac {4 \left (-x^3+x^4\right )^{3/4}}{3 x^3} \]
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Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2039} \[ \int \frac {1}{x \sqrt [4]{-x^3+x^4}} \, dx=\frac {4 \left (x^4-x^3\right )^{3/4}}{3 x^3} \]
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Rule 2039
Rubi steps \begin{align*} \text {integral}& = \frac {4 \left (-x^3+x^4\right )^{3/4}}{3 x^3} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {1}{x \sqrt [4]{-x^3+x^4}} \, dx=\frac {4 (-1+x)}{3 \sqrt [4]{(-1+x) x^3}} \]
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Time = 0.80 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75
method | result | size |
risch | \(\frac {\frac {4 x}{3}-\frac {4}{3}}{\left (x^{3} \left (x -1\right )\right )^{\frac {1}{4}}}\) | \(15\) |
pseudoelliptic | \(\frac {4 \left (x^{3} \left (x -1\right )\right )^{\frac {3}{4}}}{3 x^{3}}\) | \(15\) |
gosper | \(\frac {\frac {4 x}{3}-\frac {4}{3}}{\left (x^{4}-x^{3}\right )^{\frac {1}{4}}}\) | \(17\) |
trager | \(\frac {4 \left (x^{4}-x^{3}\right )^{\frac {3}{4}}}{3 x^{3}}\) | \(17\) |
meijerg | \(-\frac {4 \left (-\operatorname {signum}\left (x -1\right )\right )^{\frac {1}{4}} \left (1-x \right )^{\frac {3}{4}}}{3 \operatorname {signum}\left (x -1\right )^{\frac {1}{4}} x^{\frac {3}{4}}}\) | \(27\) |
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none
Time = 0.23 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1}{x \sqrt [4]{-x^3+x^4}} \, dx=\frac {4 \, {\left (x^{4} - x^{3}\right )}^{\frac {3}{4}}}{3 \, x^{3}} \]
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\[ \int \frac {1}{x \sqrt [4]{-x^3+x^4}} \, dx=\int \frac {1}{x \sqrt [4]{x^{3} \left (x - 1\right )}}\, dx \]
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\[ \int \frac {1}{x \sqrt [4]{-x^3+x^4}} \, dx=\int { \frac {1}{{\left (x^{4} - x^{3}\right )}^{\frac {1}{4}} x} \,d x } \]
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none
Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.55 \[ \int \frac {1}{x \sqrt [4]{-x^3+x^4}} \, dx=\frac {4}{3} \, {\left (-\frac {1}{x} + 1\right )}^{\frac {3}{4}} \]
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Time = 5.08 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {1}{x \sqrt [4]{-x^3+x^4}} \, dx=\frac {4\,{\left (x^4-x^3\right )}^{3/4}}{3\,x^3} \]
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