Solve the following differential equations: `(dy)/(dx)=sin^3xcos^2x+x e^x`

Explanation

Given

`(dy)/(dx)=sin^3xcos^2x+x e^x`

`(dy)=(sin^3xcos^2x+x e^x)dx`

`int(dy)=intsin^3xcos^2xdx+intx e^xdx`

Let `I_1=intsin^3xcos^2xdx`

Take `cosx=t implies -sinxdx=dt`

Then

`I_1=int(1-t^2)t^2(-dt)`

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