Optimal. Leaf size=23 \[ \left (4-x-\frac {x^2}{25}\right ) \left (-7-e^x+x+\log (x)\right ) \]
________________________________________________________________________________________
Rubi [B] time = 0.10, antiderivative size = 55, normalized size of antiderivative = 2.39, number of steps used = 17, number of rules used = 6, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {12, 14, 2196, 2194, 2176, 2313} \begin {gather*} -\frac {x^3}{25}+\frac {e^x x^2}{25}-\frac {18 x^2}{25}-\frac {1}{25} \left (x^2+25 x\right ) \log (x)+e^x x+11 x-4 e^x+4 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 2176
Rule 2194
Rule 2196
Rule 2313
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{x} \, dx\\ &=\frac {1}{25} \int \left (e^x \left (-75+27 x+x^2\right )+\frac {100+250 x-37 x^2-3 x^3-25 x \log (x)-2 x^2 \log (x)}{x}\right ) \, dx\\ &=\frac {1}{25} \int e^x \left (-75+27 x+x^2\right ) \, dx+\frac {1}{25} \int \frac {100+250 x-37 x^2-3 x^3-25 x \log (x)-2 x^2 \log (x)}{x} \, dx\\ &=\frac {1}{25} \int \left (-75 e^x+27 e^x x+e^x x^2\right ) \, dx+\frac {1}{25} \int \left (\frac {100+250 x-37 x^2-3 x^3}{x}-(25+2 x) \log (x)\right ) \, dx\\ &=\frac {1}{25} \int e^x x^2 \, dx+\frac {1}{25} \int \frac {100+250 x-37 x^2-3 x^3}{x} \, dx-\frac {1}{25} \int (25+2 x) \log (x) \, dx+\frac {27}{25} \int e^x x \, dx-3 \int e^x \, dx\\ &=-3 e^x+\frac {27 e^x x}{25}+\frac {e^x x^2}{25}-\frac {1}{25} \left (25 x+x^2\right ) \log (x)+\frac {1}{25} \int (25+x) \, dx+\frac {1}{25} \int \left (250+\frac {100}{x}-37 x-3 x^2\right ) \, dx-\frac {2}{25} \int e^x x \, dx-\frac {27 \int e^x \, dx}{25}\\ &=-\frac {102 e^x}{25}+11 x+e^x x-\frac {18 x^2}{25}+\frac {e^x x^2}{25}-\frac {x^3}{25}+4 \log (x)-\frac {1}{25} \left (25 x+x^2\right ) \log (x)+\frac {2 \int e^x \, dx}{25}\\ &=-4 e^x+11 x+e^x x-\frac {18 x^2}{25}+\frac {e^x x^2}{25}-\frac {x^3}{25}+4 \log (x)-\frac {1}{25} \left (25 x+x^2\right ) \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.07, size = 42, normalized size = 1.83 \begin {gather*} \frac {1}{25} \left (275 x-18 x^2-x^3+e^x \left (-100+25 x+x^2\right )+100 \log (x)-x (25+x) \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.61, size = 38, normalized size = 1.65 \begin {gather*} -\frac {1}{25} \, x^{3} - \frac {18}{25} \, x^{2} + \frac {1}{25} \, {\left (x^{2} + 25 \, x - 100\right )} e^{x} - \frac {1}{25} \, {\left (x^{2} + 25 \, x - 100\right )} \log \relax (x) + 11 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.27, size = 45, normalized size = 1.96 \begin {gather*} -\frac {1}{25} \, x^{3} + \frac {1}{25} \, x^{2} e^{x} - \frac {1}{25} \, x^{2} \log \relax (x) - \frac {18}{25} \, x^{2} + x e^{x} - x \log \relax (x) + 11 \, x - 4 \, e^{x} + 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.03, size = 46, normalized size = 2.00
method | result | size |
default | \(-\frac {x^{2} \ln \relax (x )}{25}-\frac {18 x^{2}}{25}-x \ln \relax (x )+11 x +\frac {{\mathrm e}^{x} x^{2}}{25}+{\mathrm e}^{x} x -4 \,{\mathrm e}^{x}-\frac {x^{3}}{25}+4 \ln \relax (x )\) | \(46\) |
norman | \(-\frac {x^{2} \ln \relax (x )}{25}-\frac {18 x^{2}}{25}-x \ln \relax (x )+11 x +\frac {{\mathrm e}^{x} x^{2}}{25}+{\mathrm e}^{x} x -4 \,{\mathrm e}^{x}-\frac {x^{3}}{25}+4 \ln \relax (x )\) | \(46\) |
risch | \(\frac {\left (-x^{2}-25 x \right ) \ln \relax (x )}{25}-\frac {x^{3}}{25}+\frac {{\mathrm e}^{x} x^{2}}{25}-\frac {18 x^{2}}{25}+{\mathrm e}^{x} x +4 \ln \relax (x )+11 x -4 \,{\mathrm e}^{x}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.44, size = 53, normalized size = 2.30 \begin {gather*} -\frac {1}{25} \, x^{3} - \frac {1}{25} \, x^{2} \log \relax (x) - \frac {18}{25} \, x^{2} + \frac {1}{25} \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} + \frac {27}{25} \, {\left (x - 1\right )} e^{x} - x \log \relax (x) + 11 \, x - 3 \, e^{x} + 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.67, size = 45, normalized size = 1.96 \begin {gather*} 11\,x-4\,{\mathrm {e}}^x+4\,\ln \relax (x)+\frac {x^2\,{\mathrm {e}}^x}{25}-\frac {x^2\,\ln \relax (x)}{25}+x\,{\mathrm {e}}^x-x\,\ln \relax (x)-\frac {18\,x^2}{25}-\frac {x^3}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.32, size = 44, normalized size = 1.91 \begin {gather*} - \frac {x^{3}}{25} - \frac {18 x^{2}}{25} + 11 x + \left (- \frac {x^{2}}{25} - x\right ) \log {\relax (x )} + \frac {\left (x^{2} + 25 x - 100\right ) e^{x}}{25} + 4 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________