Optimal. Leaf size=29 \[ x-\log \left (\left (e^x+x\right )^2-\frac {1}{5} x (3-x+4 \log (2 x))\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 1.45, 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 {-7+10 e^x+5 e^{2 x}+15 x-6 x^2+(-4+4 x) \log (2 x)}{-5 e^{2 x}+3 x-10 e^x x-6 x^2+4 x \log (2 x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {7-10 e^x-18 x+10 e^x x+12 x^2+4 \log (2 x)-8 x \log (2 x)}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)}\right ) \, dx\\ &=-x+\int \frac {7-10 e^x-18 x+10 e^x x+12 x^2+4 \log (2 x)-8 x \log (2 x)}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)} \, dx\\ &=-x+\int \left (\frac {7}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)}-\frac {10 e^x}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)}-\frac {18 x}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)}+\frac {10 e^x x}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)}+\frac {12 x^2}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)}-\frac {8 x \log (2 x)}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)}-\frac {4 \log (2 x)}{-5 e^{2 x}+3 x-10 e^x x-6 x^2+4 x \log (2 x)}\right ) \, dx\\ &=-x-4 \int \frac {\log (2 x)}{-5 e^{2 x}+3 x-10 e^x x-6 x^2+4 x \log (2 x)} \, dx+7 \int \frac {1}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)} \, dx-8 \int \frac {x \log (2 x)}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)} \, dx-10 \int \frac {e^x}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)} \, dx+10 \int \frac {e^x x}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)} \, dx+12 \int \frac {x^2}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)} \, dx-18 \int \frac {x}{5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.13, size = 34, normalized size = 1.17 \begin {gather*} x-\log \left (5 e^{2 x}-3 x+10 e^x x+6 x^2-4 x \log (2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.23, size = 33, normalized size = 1.14
method | result | size |
norman | \(x -\ln \left (10 \,{\mathrm e}^{x} x -4 x \ln \left (2 x \right )+6 x^{2}+5 \,{\mathrm e}^{2 x}-3 x \right )\) | \(33\) |
risch | \(x -\ln \left (x \right )-\ln \left (\ln \left (2 x \right )-\frac {6 x^{2}+10 \,{\mathrm e}^{x} x +5 \,{\mathrm e}^{2 x}-3 x}{4 x}\right )\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.52, size = 34, normalized size = 1.17 \begin {gather*} x - \log \left (\frac {6}{5} \, x^{2} - \frac {1}{5} \, x {\left (4 \, \log \left (2\right ) + 3\right )} + 2 \, x e^{x} - \frac {4}{5} \, x \log \left (x\right ) + e^{\left (2 \, x\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.41, size = 43, normalized size = 1.48 \begin {gather*} x - \log \left (2 \, x\right ) - \log \left (-\frac {6 \, x^{2} + 10 \, x e^{x} - 4 \, x \log \left (2 \, x\right ) - 3 \, x + 5 \, e^{\left (2 \, x\right )}}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.16, size = 36, normalized size = 1.24 \begin {gather*} x - \log {\left (\frac {6 x^{2}}{5} + 2 x e^{x} - \frac {4 x \log {\left (2 x \right )}}{5} - \frac {3 x}{5} + e^{2 x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 32, normalized size = 1.10 \begin {gather*} x - \log \left (6 \, x^{2} + 10 \, x e^{x} - 4 \, x \log \left (2 \, x\right ) - 3 \, x + 5 \, e^{\left (2 \, x\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.37, size = 32, normalized size = 1.10 \begin {gather*} x-\ln \left (5\,{\mathrm {e}}^{2\,x}-3\,x-4\,x\,\ln \left (2\,x\right )+10\,x\,{\mathrm {e}}^x+6\,x^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________