Integrand size = 17, antiderivative size = 20 \[ \int \frac {\sqrt [4]{-x^3+x^4}}{x^3} \, dx=\frac {4 \left (-x^3+x^4\right )^{5/4}}{5 x^5} \]
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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} \[ \int \frac {\sqrt [4]{-x^3+x^4}}{x^3} \, dx=\frac {4 \left (x^4-x^3\right )^{5/4}}{5 x^5} \]
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Rule 2039
Rubi steps \begin{align*} \text {integral}& = \frac {4 \left (-x^3+x^4\right )^{5/4}}{5 x^5} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {\sqrt [4]{-x^3+x^4}}{x^3} \, dx=\frac {4 \left ((-1+x) x^3\right )^{5/4}}{5 x^5} \]
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Time = 0.80 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90
method | result | size |
pseudoelliptic | \(\frac {4 \left (x -1\right ) \left (x^{3} \left (x -1\right )\right )^{\frac {1}{4}}}{5 x^{2}}\) | \(18\) |
gosper | \(\frac {4 \left (x -1\right ) \left (x^{4}-x^{3}\right )^{\frac {1}{4}}}{5 x^{2}}\) | \(20\) |
trager | \(\frac {4 \left (x -1\right ) \left (x^{4}-x^{3}\right )^{\frac {1}{4}}}{5 x^{2}}\) | \(20\) |
meijerg | \(-\frac {4 \operatorname {signum}\left (x -1\right )^{\frac {1}{4}} \left (1-x \right )^{\frac {5}{4}}}{5 \left (-\operatorname {signum}\left (x -1\right )\right )^{\frac {1}{4}} x^{\frac {5}{4}}}\) | \(27\) |
risch | \(\frac {4 \left (x^{3} \left (x -1\right )\right )^{\frac {1}{4}} \left (x^{2}-2 x +1\right )}{5 x^{2} \left (x -1\right )}\) | \(28\) |
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none
Time = 0.24 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {\sqrt [4]{-x^3+x^4}}{x^3} \, dx=\frac {4 \, {\left (x^{4} - x^{3}\right )}^{\frac {1}{4}} {\left (x - 1\right )}}{5 \, x^{2}} \]
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\[ \int \frac {\sqrt [4]{-x^3+x^4}}{x^3} \, dx=\int \frac {\sqrt [4]{x^{3} \left (x - 1\right )}}{x^{3}}\, dx \]
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\[ \int \frac {\sqrt [4]{-x^3+x^4}}{x^3} \, dx=\int { \frac {{\left (x^{4} - x^{3}\right )}^{\frac {1}{4}}}{x^{3}} \,d x } \]
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none
Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.55 \[ \int \frac {\sqrt [4]{-x^3+x^4}}{x^3} \, dx=\frac {4}{5} \, {\left (-\frac {1}{x} + 1\right )}^{\frac {5}{4}} \]
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Time = 5.02 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.65 \[ \int \frac {\sqrt [4]{-x^3+x^4}}{x^3} \, dx=\frac {4\,x\,{\left (x^4-x^3\right )}^{1/4}-4\,{\left (x^4-x^3\right )}^{1/4}}{5\,x^2} \]
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