Optimal. Leaf size=27 \[ \frac {e^{-e^4} \left (e^3-\frac {e^{10} (x+\log (x))}{x^3}\right )}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.05, antiderivative size = 44, normalized size of antiderivative = 1.63, number of steps
used = 6, number of rules used = 3, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 14, 2341}
\begin {gather*} -\frac {e^{10-e^4} \log (x)}{x^4}-\frac {e^{10-e^4}}{x^3}+\frac {e^{3-e^4}}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-e^4} \int \frac {-e^3 x^3+e^{10} (-1+3 x)+4 e^{10} \log (x)}{x^5} \, dx\\ &=e^{-e^4} \int \left (\frac {e^3 \left (-e^7+3 e^7 x-x^3\right )}{x^5}+\frac {4 e^{10} \log (x)}{x^5}\right ) \, dx\\ &=e^{3-e^4} \int \frac {-e^7+3 e^7 x-x^3}{x^5} \, dx+\left (4 e^{10-e^4}\right ) \int \frac {\log (x)}{x^5} \, dx\\ &=-\frac {e^{10-e^4}}{4 x^4}-\frac {e^{10-e^4} \log (x)}{x^4}+e^{3-e^4} \int \left (-\frac {e^7}{x^5}+\frac {3 e^7}{x^4}-\frac {1}{x^2}\right ) \, dx\\ &=-\frac {e^{10-e^4}}{x^3}+\frac {e^{3-e^4}}{x}-\frac {e^{10-e^4} \log (x)}{x^4}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 33, normalized size = 1.22 \begin {gather*} -e^{3-e^4} \left (\frac {e^7}{x^3}-\frac {1}{x}+\frac {e^7 \log (x)}{x^4}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.46, size = 51, normalized size = 1.89
method | result | size |
risch | \(-\frac {\ln \left (x \right ) {\mathrm e}^{-{\mathrm e}^{4}+10}}{x^{4}}-\frac {\left ({\mathrm e}^{7}-x^{2}\right ) {\mathrm e}^{3-{\mathrm e}^{4}}}{x^{3}}\) | \(36\) |
norman | \(\frac {{\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{3} x^{3}-{\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{10} x -{\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{10} \ln \left (x \right )}{x^{4}}\) | \(42\) |
default | \({\mathrm e}^{-{\mathrm e}^{4}} \left (\frac {{\mathrm e}^{3}}{x}+4 \,{\mathrm e}^{10} \left (-\frac {\ln \left (x \right )}{4 x^{4}}-\frac {1}{16 x^{4}}\right )-\frac {{\mathrm e}^{10}}{x^{3}}+\frac {{\mathrm e}^{10}}{4 x^{4}}\right )\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 43, normalized size = 1.59 \begin {gather*} -\frac {1}{4} \, {\left ({\left (\frac {4 \, \log \left (x\right )}{x^{4}} + \frac {1}{x^{4}}\right )} e^{10} - \frac {4 \, e^{3}}{x} + \frac {4 \, e^{10}}{x^{3}} - \frac {e^{10}}{x^{4}}\right )} e^{\left (-e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 27, normalized size = 1.00 \begin {gather*} \frac {{\left (x^{3} e^{3} - x e^{10} - e^{10} \log \left (x\right )\right )} e^{\left (-e^{4}\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.11, size = 34, normalized size = 1.26 \begin {gather*} - \frac {- x^{2} e^{3} + e^{10}}{x^{3} e^{e^{4}}} - \frac {e^{10} \log {\left (x \right )}}{x^{4} e^{e^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 27, normalized size = 1.00 \begin {gather*} \frac {{\left (x^{3} e^{3} - x e^{10} - e^{10} \log \left (x\right )\right )} e^{\left (-e^{4}\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 8.11, size = 37, normalized size = 1.37 \begin {gather*} -\frac {x\,{\mathrm {e}}^{10-{\mathrm {e}}^4}-x^3\,{\mathrm {e}}^{3-{\mathrm {e}}^4}+{\mathrm {e}}^{10-{\mathrm {e}}^4}\,\ln \left (x\right )}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________