Integrand size = 13, antiderivative size = 15 \[ \int \frac {f^{a+\frac {b}{x^3}}}{x} \, dx=-\frac {1}{3} f^a \operatorname {ExpIntegralEi}\left (\frac {b \log (f)}{x^3}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2241} \[ \int \frac {f^{a+\frac {b}{x^3}}}{x} \, dx=-\frac {1}{3} f^a \operatorname {ExpIntegralEi}\left (\frac {b \log (f)}{x^3}\right ) \]
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Rule 2241
Rubi steps \begin{align*} \text {integral}& = -\frac {1}{3} f^a \text {Ei}\left (\frac {b \log (f)}{x^3}\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {f^{a+\frac {b}{x^3}}}{x} \, dx=-\frac {1}{3} f^a \operatorname {ExpIntegralEi}\left (\frac {b \log (f)}{x^3}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(40\) vs. \(2(13)=26\).
Time = 0.04 (sec) , antiderivative size = 41, normalized size of antiderivative = 2.73
method | result | size |
meijerg | \(-\frac {f^{a} \left (-3 \ln \left (x \right )+\ln \left (-b \right )+\ln \left (\ln \left (f \right )\right )-\ln \left (-\frac {b \ln \left (f \right )}{x^{3}}\right )-\operatorname {Ei}_{1}\left (-\frac {b \ln \left (f \right )}{x^{3}}\right )\right )}{3}\) | \(41\) |
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none
Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {f^{a+\frac {b}{x^3}}}{x} \, dx=-\frac {1}{3} \, f^{a} {\rm Ei}\left (\frac {b \log \left (f\right )}{x^{3}}\right ) \]
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\[ \int \frac {f^{a+\frac {b}{x^3}}}{x} \, dx=\int \frac {f^{a + \frac {b}{x^{3}}}}{x}\, dx \]
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none
Time = 0.22 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {f^{a+\frac {b}{x^3}}}{x} \, dx=-\frac {1}{3} \, f^{a} {\rm Ei}\left (\frac {b \log \left (f\right )}{x^{3}}\right ) \]
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\[ \int \frac {f^{a+\frac {b}{x^3}}}{x} \, dx=\int { \frac {f^{a + \frac {b}{x^{3}}}}{x} \,d x } \]
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Time = 0.16 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {f^{a+\frac {b}{x^3}}}{x} \, dx=-\frac {f^a\,\mathrm {ei}\left (\frac {b\,\ln \left (f\right )}{x^3}\right )}{3} \]
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