Solve this integral please!

integrate e^(tan^-1 x)*[(1+x+x^2)/(1+x^2)]

Note : ∫ ℯ ͧ .[ ƒ(u) + ƒ'(u) ] du = ℯ ͧ .ƒ(u) .................. (1)
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I = ∫ e^( tanֿ¹ x ) · [ ( 1 + x + x² ) / ( 1 + x² ) ] dx

I = ∫ e^( tanֿ¹ x ) · ( 1 + x + x² ) · [ 1 / ( 1 + x² ) ] dx .............. (2)
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Let : u = tanֿ¹ x.

Then : du/dx = 1 / ( 1 + x² )

. and : [ 1 / ( 1 + x² ) ] dx = du.

Also : x = tan u

so that : 1 + x + x² = 1 + tan u + tan² u

. . . . . . . . . . . . . . .= tan u + ( 1 + tan² u )

. . . . . . . . . . . . . . .= tan u + sec² u.
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From (2), then,

I = ∫ ℯ ͧ . ( tan u + sec² u ) du

= ∫ ℯ ͧ .[ ƒ(u) + ƒ'(u) ] du, .............. ƒ(u) = tan u

= ℯ ͧ .ƒ(u) + C ............................... from (1)

= [ e^( tanֿ¹ x ) ]· tan u + C

= [ e^( tanֿ¹ x ) ]· x + C

= x·[ e^( tanֿ¹ x ) ] + C ....................... Ans.
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