Integrand size = 44, antiderivative size = 25 \[ \int \frac {7 e^5+e^{e^3} (-1+x)+e^{e^3} (3-x) \log (-3+x)}{(-21+7 x) \log ^2(-3+x)} \, dx=\frac {-e^5-\frac {1}{7} e^{e^3} (-1+x)}{\log (-3+x)} \]
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Time = 0.32 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.76, number of steps used = 11, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {6874, 2458, 2395, 2334, 2335, 2339, 30, 2436} \[ \int \frac {7 e^5+e^{e^3} (-1+x)+e^{e^3} (3-x) \log (-3+x)}{(-21+7 x) \log ^2(-3+x)} \, dx=\frac {e^{e^3} (3-x)}{7 \log (x-3)}-\frac {7 e^5+2 e^{e^3}}{7 \log (x-3)} \]
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Rule 30
Rule 2334
Rule 2335
Rule 2339
Rule 2395
Rule 2436
Rule 2458
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {7 e^5-e^{e^3}+e^{e^3} x}{7 (-3+x) \log ^2(-3+x)}-\frac {e^{e^3}}{7 \log (-3+x)}\right ) \, dx \\ & = \frac {1}{7} \int \frac {7 e^5-e^{e^3}+e^{e^3} x}{(-3+x) \log ^2(-3+x)} \, dx-\frac {1}{7} e^{e^3} \int \frac {1}{\log (-3+x)} \, dx \\ & = \frac {1}{7} \text {Subst}\left (\int \frac {7 e^5+2 e^{e^3}+e^{e^3} x}{x \log ^2(x)} \, dx,x,-3+x\right )-\frac {1}{7} e^{e^3} \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,-3+x\right ) \\ & = -\frac {1}{7} e^{e^3} \operatorname {LogIntegral}(-3+x)+\frac {1}{7} \text {Subst}\left (\int \left (\frac {e^{e^3}}{\log ^2(x)}+\frac {7 e^5+2 e^{e^3}}{x \log ^2(x)}\right ) \, dx,x,-3+x\right ) \\ & = -\frac {1}{7} e^{e^3} \operatorname {LogIntegral}(-3+x)+\frac {1}{7} e^{e^3} \text {Subst}\left (\int \frac {1}{\log ^2(x)} \, dx,x,-3+x\right )+\frac {1}{7} \left (7 e^5+2 e^{e^3}\right ) \text {Subst}\left (\int \frac {1}{x \log ^2(x)} \, dx,x,-3+x\right ) \\ & = \frac {e^{e^3} (3-x)}{7 \log (-3+x)}-\frac {1}{7} e^{e^3} \operatorname {LogIntegral}(-3+x)+\frac {1}{7} e^{e^3} \text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,-3+x\right )+\frac {1}{7} \left (7 e^5+2 e^{e^3}\right ) \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (-3+x)\right ) \\ & = -\frac {7 e^5+2 e^{e^3}}{7 \log (-3+x)}+\frac {e^{e^3} (3-x)}{7 \log (-3+x)} \\ \end{align*}
Time = 0.23 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {7 e^5+e^{e^3} (-1+x)+e^{e^3} (3-x) \log (-3+x)}{(-21+7 x) \log ^2(-3+x)} \, dx=-\frac {7 e^5+e^{e^3} (-1+x)}{7 \log (-3+x)} \]
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Time = 0.20 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96
method | result | size |
norman | \(\frac {-\frac {x \,{\mathrm e}^{{\mathrm e}^{3}}}{7}+\frac {{\mathrm e}^{{\mathrm e}^{3}}}{7}-{\mathrm e}^{5}}{\ln \left (-3+x \right )}\) | \(24\) |
risch | \(-\frac {7 \,{\mathrm e}^{5}+x \,{\mathrm e}^{{\mathrm e}^{3}}-{\mathrm e}^{{\mathrm e}^{3}}}{7 \ln \left (-3+x \right )}\) | \(24\) |
parallelrisch | \(-\frac {7 \,{\mathrm e}^{5}+x \,{\mathrm e}^{{\mathrm e}^{3}}-{\mathrm e}^{{\mathrm e}^{3}}}{7 \ln \left (-3+x \right )}\) | \(24\) |
derivativedivides | \(\frac {{\mathrm e}^{{\mathrm e}^{3}} \operatorname {Ei}_{1}\left (-\ln \left (-3+x \right )\right )}{7}+\frac {{\mathrm e}^{{\mathrm e}^{3}} \left (-\frac {-3+x}{\ln \left (-3+x \right )}-\operatorname {Ei}_{1}\left (-\ln \left (-3+x \right )\right )\right )}{7}-\frac {{\mathrm e}^{5}}{\ln \left (-3+x \right )}-\frac {2 \,{\mathrm e}^{{\mathrm e}^{3}}}{7 \ln \left (-3+x \right )}\) | \(63\) |
default | \(\frac {{\mathrm e}^{{\mathrm e}^{3}} \operatorname {Ei}_{1}\left (-\ln \left (-3+x \right )\right )}{7}+\frac {{\mathrm e}^{{\mathrm e}^{3}} \left (-\frac {-3+x}{\ln \left (-3+x \right )}-\operatorname {Ei}_{1}\left (-\ln \left (-3+x \right )\right )\right )}{7}-\frac {{\mathrm e}^{5}}{\ln \left (-3+x \right )}-\frac {2 \,{\mathrm e}^{{\mathrm e}^{3}}}{7 \ln \left (-3+x \right )}\) | \(63\) |
parts | \(\frac {{\mathrm e}^{{\mathrm e}^{3}} \operatorname {Ei}_{1}\left (-\ln \left (-3+x \right )\right )}{7}+\frac {{\mathrm e}^{{\mathrm e}^{3}} \left (-\frac {-3+x}{\ln \left (-3+x \right )}-\operatorname {Ei}_{1}\left (-\ln \left (-3+x \right )\right )\right )}{7}-\frac {{\mathrm e}^{5}}{\ln \left (-3+x \right )}-\frac {2 \,{\mathrm e}^{{\mathrm e}^{3}}}{7 \ln \left (-3+x \right )}\) | \(63\) |
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Time = 0.23 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80 \[ \int \frac {7 e^5+e^{e^3} (-1+x)+e^{e^3} (3-x) \log (-3+x)}{(-21+7 x) \log ^2(-3+x)} \, dx=-\frac {{\left (x - 1\right )} e^{\left (e^{3}\right )} + 7 \, e^{5}}{7 \, \log \left (x - 3\right )} \]
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Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {7 e^5+e^{e^3} (-1+x)+e^{e^3} (3-x) \log (-3+x)}{(-21+7 x) \log ^2(-3+x)} \, dx=\frac {- x e^{e^{3}} - 7 e^{5} + e^{e^{3}}}{7 \log {\left (x - 3 \right )}} \]
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Time = 0.23 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.56 \[ \int \frac {7 e^5+e^{e^3} (-1+x)+e^{e^3} (3-x) \log (-3+x)}{(-21+7 x) \log ^2(-3+x)} \, dx=-\frac {x e^{\left (e^{3}\right )}}{7 \, \log \left (x - 3\right )} - \frac {e^{5}}{\log \left (x - 3\right )} + \frac {e^{\left (e^{3}\right )}}{7 \, \log \left (x - 3\right )} - \frac {3}{7} \, e^{\left (e^{3}\right )} \]
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Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {7 e^5+e^{e^3} (-1+x)+e^{e^3} (3-x) \log (-3+x)}{(-21+7 x) \log ^2(-3+x)} \, dx=-\frac {x e^{\left (e^{3}\right )} + 7 \, e^{5} - e^{\left (e^{3}\right )}}{7 \, \log \left (x - 3\right )} \]
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Time = 9.10 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {7 e^5+e^{e^3} (-1+x)+e^{e^3} (3-x) \log (-3+x)}{(-21+7 x) \log ^2(-3+x)} \, dx=-\frac {7\,{\mathrm {e}}^5-{\mathrm {e}}^{{\mathrm {e}}^3}+x\,{\mathrm {e}}^{{\mathrm {e}}^3}}{7\,\ln \left (x-3\right )} \]
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