Evaluate each of the following integral: `int_0^(pi//2)logtanx dx`

Explanation

Let, `{I}=int_{0}^{pi / 2} log (tan x) d x`

Using the property `int_{a}^{b} f(x) d x=int_{a}^{b} f(a+b-x) d x`, we get:-


`I=int_{0}^{pi / 2} log left(tan left(frac{pi}{2}-xright)right) d x `< br>
`Rightarrow I=int_{0}^{pi / 2} log (cot x) d x `

`=int_{0}^{pi / 2} log frac{1}{tan x} d x `

`=-int_{0}^{pi / 2} log (tan x) d x `

`I=-I `

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