Optimal. Leaf size=24 \[ 2 x-4 \left (3+e^x \left (1+e^x\right ) x\right )+\frac {\log (x)}{9} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 42, normalized size of antiderivative = 1.75, number of steps
used = 9, number of rules used = 5, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.161, Rules used = {12, 14, 2207,
2225, 45} \begin {gather*} 2 x+4 e^x+2 e^{2 x}-4 e^x (x+1)-2 e^{2 x} (2 x+1)+\frac {\log (x)}{9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 45
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \frac {1+18 x+e^x \left (-36+e^x (-36-72 x)-36 x\right ) x}{x} \, dx\\ &=\frac {1}{9} \int \left (-36 e^x (1+x)-36 e^{2 x} (1+2 x)+\frac {1+18 x}{x}\right ) \, dx\\ &=\frac {1}{9} \int \frac {1+18 x}{x} \, dx-4 \int e^x (1+x) \, dx-4 \int e^{2 x} (1+2 x) \, dx\\ &=-4 e^x (1+x)-2 e^{2 x} (1+2 x)+\frac {1}{9} \int \left (18+\frac {1}{x}\right ) \, dx+4 \int e^x \, dx+4 \int e^{2 x} \, dx\\ &=4 e^x+2 e^{2 x}+2 x-4 e^x (1+x)-2 e^{2 x} (1+2 x)+\frac {\log (x)}{9}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.04, size = 24, normalized size = 1.00 \begin {gather*} 2 x-4 e^x x-4 e^{2 x} x+\frac {\log (x)}{9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.12, size = 21, normalized size = 0.88
method | result | size |
default | \(2 x +\frac {\ln \left (x \right )}{9}-4 \,{\mathrm e}^{x} x -4 x \,{\mathrm e}^{2 x}\) | \(21\) |
norman | \(2 x +\frac {\ln \left (x \right )}{9}-4 \,{\mathrm e}^{x} x -4 x \,{\mathrm e}^{2 x}\) | \(21\) |
risch | \(2 x +\frac {\ln \left (x \right )}{9}-4 \,{\mathrm e}^{x} x -4 x \,{\mathrm e}^{2 x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.35, size = 36, normalized size = 1.50 \begin {gather*} -2 \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x - 1\right )} e^{x} + 2 \, x - 2 \, e^{\left (2 \, x\right )} - 4 \, e^{x} + \frac {1}{9} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 34, normalized size = 1.42 \begin {gather*} \frac {18 \, x^{2} - 36 \, x e^{\left (x + \log \left (x\right )\right )} + x \log \left (x\right ) - 36 \, e^{\left (2 \, x + 2 \, \log \left (x\right )\right )}}{9 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 22, normalized size = 0.92 \begin {gather*} - 4 x e^{2 x} - 4 x e^{x} + 2 x + \frac {\log {\left (x \right )}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 20, normalized size = 0.83 \begin {gather*} -4 \, x e^{\left (2 \, x\right )} - 4 \, x e^{x} + 2 \, x + \frac {1}{9} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.32, size = 20, normalized size = 0.83 \begin {gather*} 2\,x+\frac {\ln \left (x\right )}{9}-4\,x\,{\mathrm {e}}^{2\,x}-4\,x\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________