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int_(1)^(0)((tan^(-1)x)/x + (lnx)/(1+x^(2))) dx is equal to |
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Answer» `1/e_(tan^(-1)e)` `=(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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