Optimal. Leaf size=29 \[ x-5 \left (\frac {1}{4} e^{\frac {e^x}{8 x}}+x-\frac {\log (x)}{x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.32, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {160+e^{\frac {e^x}{8 x}+x} (5-5 x)-128 x^2-160 \log (x)}{32 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{32} \int \frac {160+e^{\frac {e^x}{8 x}+x} (5-5 x)-128 x^2-160 \log (x)}{x^2} \, dx\\ &=\frac {1}{32} \int \left (-\frac {5 e^{\frac {e^x}{8 x}+x} (-1+x)}{x^2}-\frac {32 \left (-5+4 x^2+5 \log (x)\right )}{x^2}\right ) \, dx\\ &=-\left (\frac {5}{32} \int \frac {e^{\frac {e^x}{8 x}+x} (-1+x)}{x^2} \, dx\right )-\int \frac {-5+4 x^2+5 \log (x)}{x^2} \, dx\\ &=-\left (\frac {5}{32} \int \left (-\frac {e^{\frac {e^x}{8 x}+x}}{x^2}+\frac {e^{\frac {e^x}{8 x}+x}}{x}\right ) \, dx\right )-\int \left (\frac {-5+4 x^2}{x^2}+\frac {5 \log (x)}{x^2}\right ) \, dx\\ &=\frac {5}{32} \int \frac {e^{\frac {e^x}{8 x}+x}}{x^2} \, dx-\frac {5}{32} \int \frac {e^{\frac {e^x}{8 x}+x}}{x} \, dx-5 \int \frac {\log (x)}{x^2} \, dx-\int \frac {-5+4 x^2}{x^2} \, dx\\ &=\frac {5}{x}+\frac {5 \log (x)}{x}+\frac {5}{32} \int \frac {e^{\frac {e^x}{8 x}+x}}{x^2} \, dx-\frac {5}{32} \int \frac {e^{\frac {e^x}{8 x}+x}}{x} \, dx-\int \left (4-\frac {5}{x^2}\right ) \, dx\\ &=-4 x+\frac {5 \log (x)}{x}+\frac {5}{32} \int \frac {e^{\frac {e^x}{8 x}+x}}{x^2} \, dx-\frac {5}{32} \int \frac {e^{\frac {e^x}{8 x}+x}}{x} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.10, size = 27, normalized size = 0.93 \begin {gather*} -\frac {5}{4} e^{\frac {e^x}{8 x}}-4 x+\frac {5 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.12, size = 24, normalized size = 0.83
method | result | size |
risch | \(-4 x -\frac {5 \,{\mathrm e}^{\frac {{\mathrm e}^{x}}{8 x}}}{4}+\frac {5 \ln \left (x \right )}{x}\) | \(22\) |
default | \(-4 x -\frac {5 \,{\mathrm e}^{\frac {{\mathrm e}^{x}}{8 x}}}{4}+\frac {5 \ln \left (x \right )}{x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.32, size = 30, normalized size = 1.03 \begin {gather*} -4 \, x - \frac {5 \, {\left (x e^{\left (\frac {e^{x}}{8 \, x}\right )} - 4 \, \log \left (x\right ) - 4\right )}}{4 \, x} - \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 40, normalized size = 1.38 \begin {gather*} -\frac {{\left (16 \, x^{2} e^{x} + 5 \, x e^{\left (\frac {8 \, x^{2} + e^{x}}{8 \, x}\right )} - 20 \, e^{x} \log \left (x\right )\right )} e^{\left (-x\right )}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.16, size = 20, normalized size = 0.69 \begin {gather*} - 4 x - \frac {5 e^{\frac {e^{x}}{8 x}}}{4} + \frac {5 \log {\left (x \right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 40, normalized size = 1.38 \begin {gather*} -\frac {{\left (16 \, x^{2} e^{x} + 5 \, x e^{\left (\frac {8 \, x^{2} + e^{x}}{8 \, x}\right )} - 20 \, e^{x} \log \left (x\right )\right )} e^{\left (-x\right )}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 7.77, size = 21, normalized size = 0.72 \begin {gather*} \frac {5\,\ln \left (x\right )}{x}-\frac {5\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{8\,x}}}{4}-4\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________