u = tan x , du = sec^2x dx
S u e^u du
integrate by parts
f= u , df=du
dg= e^u du, g = e^u
integral = fg - integral (g df) = u e^u - integral e^u du
= u e^u - e^u + c
integral =tan x e^tan x - e^tan x + c
e^tan x ( tan x - 1) + c
e^Tan[x] (-1 + Tan[x])
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u = tan x , du = sec^2x dx
S u e^u du
integrate by parts
f= u , df=du
dg= e^u du, g = e^u
integral = fg - integral (g df) = u e^u - integral e^u du
= u e^u - e^u + c
integral =tan x e^tan x - e^tan x + c
e^tan x ( tan x - 1) + c
e^Tan[x] (-1 + Tan[x])