Integrate : ex(x2+1/(x+1)2)dx

Let I = exx2 + 1x+12 dx=exx2 - 1 + 2x+12 dx=ex x+1x-1 + 2x+12 dx=exx-1x+1 dx + 2exx+12 dx=x-1x+1 × ex dx - ddxx-1x+1 ×ex dx  dx +  2exx+12 dx=x-1x+1 ex - x+1×1 - x-1×1x+12 ex dx + 2exx+12 dx=exx-1x+1 -2exx+12 dx  + 2exx+12 dx=exx-1x+1 + C

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