Integrand size = 43, antiderivative size = 18 \[ \int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx=\frac {e^{-29-2 x+\frac {\log (x)}{\log (4)}}}{x} \]
[Out]
Time = 0.12 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {12, 2306, 2228} \[ \int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx=e^{-2 x-29} x^{\frac {1}{\log (4)}-1} \]
[In]
[Out]
Rule 12
Rule 2228
Rule 2306
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {\exp \left (\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}\right ) (1+(-1-2 x) \log (4))}{x} \, dx}{\log (4)} \\ & = \frac {\int e^{-29-2 x} x^{-1+\frac {1-\log (4)}{\log (4)}} (1+(-1-2 x) \log (4)) \, dx}{\log (4)} \\ & = e^{-29-2 x} x^{-1+\frac {1}{\log (4)}} \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.39 \[ \int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx=\frac {e^{-29-2 x} x^{-1+\frac {1}{\log (4)}} \log (16)}{2 \log (4)} \]
[In]
[Out]
Time = 0.22 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06
method | result | size |
risch | \(\frac {x^{\frac {1}{2 \ln \left (2\right )}} {\mathrm e}^{-2 x -29}}{x}\) | \(19\) |
norman | \({\mathrm e}^{\frac {\left (1-2 \ln \left (2\right )\right ) \ln \left (x \right )+2 \left (-2 x -29\right ) \ln \left (2\right )}{2 \ln \left (2\right )}}\) | \(27\) |
parallelrisch | \({\mathrm e}^{\frac {\left (1-2 \ln \left (2\right )\right ) \ln \left (x \right )+2 \left (-2 x -29\right ) \ln \left (2\right )}{2 \ln \left (2\right )}}\) | \(27\) |
gosper | \({\mathrm e}^{-\frac {2 \ln \left (2\right ) \ln \left (x \right )+4 x \ln \left (2\right )-\ln \left (x \right )+58 \ln \left (2\right )}{2 \ln \left (2\right )}}\) | \(28\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.44 \[ \int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx=e^{\left (-\frac {2 \, {\left (2 \, x + 29\right )} \log \left (2\right ) + {\left (2 \, \log \left (2\right ) - 1\right )} \log \left (x\right )}{2 \, \log \left (2\right )}\right )} \]
[In]
[Out]
Time = 1.12 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx=\frac {x^{\frac {1}{2 \log {\left (2 \right )}}} e^{- 2 x}}{x e^{29}} \]
[In]
[Out]
none
Time = 0.36 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx=\frac {e^{\left (-2 \, x + \frac {\log \left (x\right )}{2 \, \log \left (2\right )} - 29\right )}}{x} \]
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx=e^{\left (-2 \, x + \frac {\log \left (x\right )}{2 \, \log \left (2\right )} - \log \left (x\right ) - 29\right )} \]
[In]
[Out]
Time = 8.44 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx=x^{\frac {1}{2\,\ln \left (2\right )}-1}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-29} \]
[In]
[Out]