Optimal. Leaf size=26 \[ e^{\frac {x \left (e^{10}-\frac {6}{5 x}-\log (25 x)\right )}{-2+x}} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 2.09, 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 {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \left (16-10 e^{10}-5 x+10 \log (25 x)\right )}{20-20 x+5 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \left (16-10 e^{10}-5 x+10 \log (25 x)\right )}{5 (-2+x)^2} \, dx\\ &=\frac {1}{5} \int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \left (16-10 e^{10}-5 x+10 \log (25 x)\right )}{(-2+x)^2} \, dx\\ &=\frac {1}{5} \int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \left (16 \left (1-\frac {5 e^{10}}{8}\right )-5 x+10 \log (25 x)\right )}{(2-x)^2} \, dx\\ &=\frac {1}{5} \int \left (\frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \left (16-10 e^{10}-5 x\right )}{(-2+x)^2}+\frac {10 e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \log (25 x)}{(-2+x)^2}\right ) \, dx\\ &=\frac {1}{5} \int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \left (16-10 e^{10}-5 x\right )}{(-2+x)^2} \, dx+2 \int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \log (25 x)}{(-2+x)^2} \, dx\\ &=\frac {1}{5} \int \left (-\frac {2 e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \left (-3+5 e^{10}\right )}{(-2+x)^2}-\frac {5 e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}}}{-2+x}\right ) \, dx+2 \int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \log (25 x)}{(-2+x)^2} \, dx\\ &=2 \int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}} \log (25 x)}{(-2+x)^2} \, dx+\frac {1}{5} \left (2 \left (3-5 e^{10}\right )\right ) \int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}}}{(-2+x)^2} \, dx-\int \frac {e^{\frac {-6+5 e^{10} x-5 x \log (25 x)}{-10+5 x}}}{-2+x} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.14, size = 44, normalized size = 1.69 \begin {gather*} 5^{-1+\frac {2+x}{2-x}} e^{\frac {6-5 e^{10} x}{10-5 x}} x^{-\frac {x}{-2+x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.58, size = 23, normalized size = 0.88
method | result | size |
risch | \({\mathrm e}^{\frac {-5 x \ln \left (25 x \right )+5 x \,{\mathrm e}^{10}-6}{5 x -10}}\) | \(23\) |
norman | \(\frac {x \,{\mathrm e}^{\frac {-5 x \ln \left (25 x \right )+5 x \,{\mathrm e}^{10}-6}{5 x -10}}-2 \,{\mathrm e}^{\frac {-5 x \ln \left (25 x \right )+5 x \,{\mathrm e}^{10}-6}{5 x -10}}}{x -2}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 22, normalized size = 0.85 \begin {gather*} e^{\left (\frac {5 \, x e^{10} - 5 \, x \log \left (25 \, x\right ) - 6}{5 \, {\left (x - 2\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.27, size = 22, normalized size = 0.85 \begin {gather*} e^{\frac {- 5 x \log {\left (25 x \right )} + 5 x e^{10} - 6}{5 x - 10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 2.50, size = 52, normalized size = 2.00 \begin {gather*} \frac {{\mathrm {e}}^{\frac {5\,x\,{\mathrm {e}}^{10}}{5\,x-10}}\,{\mathrm {e}}^{-\frac {6}{5\,x-10}}}{5^{\frac {10\,x}{5\,x-10}}\,x^{\frac {5\,x}{5\,x-10}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________