Integrand size = 20, antiderivative size = 18 \[ \int \frac {3+x^4}{x^3 \sqrt [4]{-x+x^5}} \, dx=\frac {4 \left (-x+x^5\right )^{3/4}}{3 x^3} \]
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Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {1604} \[ \int \frac {3+x^4}{x^3 \sqrt [4]{-x+x^5}} \, dx=\frac {4 \left (x^5-x\right )^{3/4}}{3 x^3} \]
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Rule 1604
Rubi steps \begin{align*} \text {integral}& = \frac {4 \left (-x+x^5\right )^{3/4}}{3 x^3} \\ \end{align*}
Time = 10.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {3+x^4}{x^3 \sqrt [4]{-x+x^5}} \, dx=\frac {4 \left (x \left (-1+x^4\right )\right )^{3/4}}{3 x^3} \]
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Time = 0.82 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83
method | result | size |
trager | \(\frac {4 \left (x^{5}-x \right )^{\frac {3}{4}}}{3 x^{3}}\) | \(15\) |
pseudoelliptic | \(\frac {4 \left (x^{5}-x \right )^{\frac {3}{4}}}{3 x^{3}}\) | \(15\) |
risch | \(\frac {\frac {4 x^{4}}{3}-\frac {4}{3}}{x^{2} {\left (x \left (x^{4}-1\right )\right )}^{\frac {1}{4}}}\) | \(20\) |
gosper | \(\frac {4 \left (x^{2}+1\right ) \left (x -1\right ) \left (1+x \right )}{3 x^{2} \left (x^{5}-x \right )^{\frac {1}{4}}}\) | \(26\) |
meijerg | \(-\frac {4 {\left (-\operatorname {signum}\left (x^{4}-1\right )\right )}^{\frac {1}{4}} \operatorname {hypergeom}\left (\left [-\frac {9}{16}, \frac {1}{4}\right ], \left [\frac {7}{16}\right ], x^{4}\right )}{3 \operatorname {signum}\left (x^{4}-1\right )^{\frac {1}{4}} x^{\frac {9}{4}}}+\frac {4 {\left (-\operatorname {signum}\left (x^{4}-1\right )\right )}^{\frac {1}{4}} x^{\frac {7}{4}} \operatorname {hypergeom}\left (\left [\frac {1}{4}, \frac {7}{16}\right ], \left [\frac {23}{16}\right ], x^{4}\right )}{7 \operatorname {signum}\left (x^{4}-1\right )^{\frac {1}{4}}}\) | \(66\) |
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none
Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {3+x^4}{x^3 \sqrt [4]{-x+x^5}} \, dx=\frac {4 \, {\left (x^{5} - x\right )}^{\frac {3}{4}}}{3 \, x^{3}} \]
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\[ \int \frac {3+x^4}{x^3 \sqrt [4]{-x+x^5}} \, dx=\int \frac {x^{4} + 3}{x^{3} \sqrt [4]{x \left (x - 1\right ) \left (x + 1\right ) \left (x^{2} + 1\right )}}\, dx \]
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\[ \int \frac {3+x^4}{x^3 \sqrt [4]{-x+x^5}} \, dx=\int { \frac {x^{4} + 3}{{\left (x^{5} - x\right )}^{\frac {1}{4}} x^{3}} \,d x } \]
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\[ \int \frac {3+x^4}{x^3 \sqrt [4]{-x+x^5}} \, dx=\int { \frac {x^{4} + 3}{{\left (x^{5} - x\right )}^{\frac {1}{4}} x^{3}} \,d x } \]
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Time = 5.07 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {3+x^4}{x^3 \sqrt [4]{-x+x^5}} \, dx=\frac {4\,{\left (x^5-x\right )}^{3/4}}{3\,x^3} \]
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