Solve x(2xe^{x}+x^{2}e^{x})sin(x^{2}e^{x}+4xe^{x}+2e^{x})+2xe^{x}+x^{2}e^x(cos(2xe^x+x^2e^x))

$$x ( 2 x e ^ { x } + x ^ { 2 } e ^ { x } ) \sin ( x ^ { 2 } e ^ { x } + 4 x e ^ { x } + 2 e ^ { x } ) + 2 x e ^ { x } + x ^ { 2 } e ^ { x } ( \cos ( 2 x e ^ { x } + x ^ { 2 } e ^ { x } ) )$$

Factor

$$xe^{x}\left(x\left(x+2\right)\sin(\left(x^{2}+4x+2\right)e^{x})+x\cos(x\left(x+2\right)e^{x})+2\right)$$

Solution Steps

Factor out x.

$$xe^{x}\left(x\left(2+x\right)\sin(e^{x}\left(x^{2}+4x+2\right))+2+x\cos(xe^{x}\left(2+x\right))\right)$$

Evaluate

$$xe^{x}\left(x\left(x+2\right)\sin(\left(x^{2}+4x+2\right)e^{x})+x\cos(x\left(x+2\right)e^{x})+2\right)$$