The value of integral _ 1 / e ^ x t 1+t^2 d t+ _ / / e ^ x d t t (1+t^2 ) is equal to

Step-by-step solution

aligned & I = _ t ₀ ^ x t 1+ t ^2 dt + _ 1₀ ^ x dt t (1+ t ^2 ) & Put t = 1 z dt = -1 z ^2 ~d . & I= _ 1 / 0 ^ x 1 1+t^2 d t+ _e^ lan x -1 z^2 z (1+ 1 z^2 ) d z & I = _ V / c ^ x t 1+ t ^2 dt - _ e ^ x z z ^2+1 dz & I= _ 1 / e ^ x t 1+t^2 d t+ _ x ^e 1 1+t^2 d t & . l = _ 1 / e ^e 1 1+ t ^2 dt = 1 2 (1+ t ^2 ) )_ 1 c ^ e & = 1 2 [ (1+ e ^2 )- (1+ 1 e ^2 ) ] & I = 1 2 [2]=1 aligned