Integrand size = 42, antiderivative size = 21 \[ \int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx=-9+e^{2 x} \left (x+x \left (6+x^{-3+6 x}\right )\right ) \]
[Out]
\[ \int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx=\int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int e^{2 x} (7+14 x) \, dx+\int x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right ) \, dx \\ & = \frac {7}{2} e^{2 x} (1+2 x)-7 \int e^{2 x} \, dx+\int 2 e^{2 x} x^{-3+6 x} (-1+4 x+3 x \log (x)) \, dx \\ & = -\frac {7 e^{2 x}}{2}+\frac {7}{2} e^{2 x} (1+2 x)+2 \int e^{2 x} x^{-3+6 x} (-1+4 x+3 x \log (x)) \, dx \\ & = -\frac {7 e^{2 x}}{2}+\frac {7}{2} e^{2 x} (1+2 x)+2 \int \left (-e^{2 x} x^{-3+6 x}+4 e^{2 x} x^{-2+6 x}+3 e^{2 x} x^{-2+6 x} \log (x)\right ) \, dx \\ & = -\frac {7 e^{2 x}}{2}+\frac {7}{2} e^{2 x} (1+2 x)-2 \int e^{2 x} x^{-3+6 x} \, dx+6 \int e^{2 x} x^{-2+6 x} \log (x) \, dx+8 \int e^{2 x} x^{-2+6 x} \, dx \\ & = -\frac {7 e^{2 x}}{2}+\frac {7}{2} e^{2 x} (1+2 x)-2 \int e^{2 x} x^{-3+6 x} \, dx-6 \int \frac {\int e^{2 x} x^{-2+6 x} \, dx}{x} \, dx+8 \int e^{2 x} x^{-2+6 x} \, dx+(6 \log (x)) \int e^{2 x} x^{-2+6 x} \, dx \\ \end{align*}
Time = 0.50 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx=\frac {e^{2 x} \left (7 x^3+x^{6 x}\right )}{x^2} \]
[In]
[Out]
Time = 0.23 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.05
method | result | size |
risch | \({\mathrm e}^{2 x} x^{-3+6 x} x +7 x \,{\mathrm e}^{2 x}\) | \(22\) |
default | \(7 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} {\mathrm e}^{\left (-3+6 x \right ) \ln \left (x \right )} x\) | \(24\) |
parallelrisch | \(7 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} {\mathrm e}^{\left (-3+6 x \right ) \ln \left (x \right )} x\) | \(24\) |
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx=x x^{6 \, x - 3} e^{\left (2 \, x\right )} + 7 \, x e^{\left (2 \, x\right )} \]
[In]
[Out]
Time = 2.82 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14 \[ \int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx=x e^{2 x} e^{\left (6 x - 3\right ) \log {\left (x \right )}} + 7 x e^{2 x} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.52 \[ \int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx=\frac {7}{2} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + \frac {e^{\left (6 \, x \log \left (x\right ) + 2 \, x\right )}}{x^{2}} + \frac {7}{2} \, e^{\left (2 \, x\right )} \]
[In]
[Out]
none
Time = 0.34 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.05 \[ \int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx=7 \, x e^{\left (2 \, x\right )} + e^{\left (6 \, x \log \left (x\right ) + 2 \, x - 2 \, \log \left (x\right )\right )} \]
[In]
[Out]
Time = 16.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \left (e^{2 x} (7+14 x)+x^{-3+6 x} \left (e^{2 x} (-2+8 x)+6 e^{2 x} x \log (x)\right )\right ) \, dx=\frac {{\mathrm {e}}^{2\,x}\,\left (x^{6\,x}+7\,x^3\right )}{x^2} \]
[In]
[Out]