1.

int_(1)^(0)((tan^(-1)x)/x + (lnx)/(1+x^(2))) dx is equal to

Answer»

`1/e_(tan^(-1)e)`
`tan^(-1)e`
`ETAN^(-1) (1/e)`
`tan^(-1)(lne)`

Solution :`int_(1)^(e)tan^(-1)X. 1/x dx + int_(1)^(e)(ln x)/(1+x^(2)) dx`
`=(tan^(-1) x ln x)_(1)^(e) - int_(1)^(e) 1/(1+x^(2)) ln dx + int_(1)^(e) (ln x)/(1+x^(2)) dx`
`=tan^(-1)(e). Lne - tan^(-1)(1).ln1`
`= tan^(-1)(e)`


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