Integrand size = 13, antiderivative size = 22 \[ \int \frac {1}{x \left (a+b x^6\right )} \, dx=\frac {\log (x)}{a}-\frac {\log \left (a+b x^6\right )}{6 a} \]
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Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.308, Rules used = {272, 36, 29, 31} \[ \int \frac {1}{x \left (a+b x^6\right )} \, dx=\frac {\log (x)}{a}-\frac {\log \left (a+b x^6\right )}{6 a} \]
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Rule 29
Rule 31
Rule 36
Rule 272
Rubi steps \begin{align*} \text {integral}& = \frac {1}{6} \text {Subst}\left (\int \frac {1}{x (a+b x)} \, dx,x,x^6\right ) \\ & = \frac {\text {Subst}\left (\int \frac {1}{x} \, dx,x,x^6\right )}{6 a}-\frac {b \text {Subst}\left (\int \frac {1}{a+b x} \, dx,x,x^6\right )}{6 a} \\ & = \frac {\log (x)}{a}-\frac {\log \left (a+b x^6\right )}{6 a} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \left (a+b x^6\right )} \, dx=\frac {\log (x)}{a}-\frac {\log \left (a+b x^6\right )}{6 a} \]
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Time = 4.48 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95
method | result | size |
default | \(\frac {\ln \left (x \right )}{a}-\frac {\ln \left (b \,x^{6}+a \right )}{6 a}\) | \(21\) |
norman | \(\frac {\ln \left (x \right )}{a}-\frac {\ln \left (b \,x^{6}+a \right )}{6 a}\) | \(21\) |
risch | \(\frac {\ln \left (x \right )}{a}-\frac {\ln \left (b \,x^{6}+a \right )}{6 a}\) | \(21\) |
parallelrisch | \(\frac {6 \ln \left (x \right )-\ln \left (b \,x^{6}+a \right )}{6 a}\) | \(21\) |
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none
Time = 0.36 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \frac {1}{x \left (a+b x^6\right )} \, dx=-\frac {\log \left (b x^{6} + a\right ) - 6 \, \log \left (x\right )}{6 \, a} \]
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Time = 0.17 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68 \[ \int \frac {1}{x \left (a+b x^6\right )} \, dx=\frac {\log {\left (x \right )}}{a} - \frac {\log {\left (\frac {a}{b} + x^{6} \right )}}{6 a} \]
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none
Time = 0.22 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {1}{x \left (a+b x^6\right )} \, dx=-\frac {\log \left (b x^{6} + a\right )}{6 \, a} + \frac {\log \left (x^{6}\right )}{6 \, a} \]
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none
Time = 0.28 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {1}{x \left (a+b x^6\right )} \, dx=\frac {\log \left (x^{6}\right )}{6 \, a} - \frac {\log \left ({\left | b x^{6} + a \right |}\right )}{6 \, a} \]
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Time = 5.66 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \frac {1}{x \left (a+b x^6\right )} \, dx=-\frac {\ln \left (b\,x^6+a\right )-6\,\ln \left (x\right )}{6\,a} \]
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