1.

int_(-1)^(1) (e^(|x|))/(1+a^(x))dx

Answer»

`e`
`2-e`
`e-3`
`e-1`

Solution :`I=int_(-1)^(1)(e^(|x|))/(1+a^(x))DX`………..
`I=int_(-1)^(1)(e^(|0-x|)/(1+a^(-x))dx` (by `int_(a)^(b)f(a+b-x)dx)`
`I=int_(-1)^(1)(a^(x).e^(|x|))/(1+a^(x))dx`………(2)
(1) `+` (2)
`2I=int_(-1)^(1)e^(|x|)dx`
`2I=2int_(0)^(1)e^(|x|)dx`
`I=int_(0)^(1)dx=e-1`


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