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Integration of 1/(1+((log)e x)^2) with r...

Integration of `1/(1+((log)_e x)^2)` with respect to `(log)_e x` is `(tan^(-1)((log)_e x)/x+C` (b) `tan^(-1)((log)_e x)+C` (c) `(tan^(-1)x)/x+C` (d) none of these

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Given,`1/(1+((log)_e x)^2)`
`int1/(1+((log)_e x)^2)d((log)_e x)`
=`intdx/(x(1+(log_e​x)^2))`
Let` t=log_e​x⇒dt=1/x​dx`
=`∫dt/(1+t^2)`
​ =`tan^(−1)t+c ...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
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