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The value of $\int_{1 / e}^{\tan x} \frac{t}{1 + t^{2}} d t + \int_{1 / e}^{\cot x} \frac{d t}{t (1 + t^{2})}$ is

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1t1+t2=1t−t1+t2So the required integral is equal to∫1etan⁡x tdx1+t2+∫1ecot⁡x dtt−∫1ecot⁡x tdt1+t2=12log⁡1+t21etan⁡x+log⁡t1ecot⁡x−12log⁡1+t21ecot⁡x=log⁡|sec⁡x|+log⁡|cot⁡x|+1−log⁡|cosec⁡x|=1

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The value of ∫1/etan⁡x t1+t2dt+∫1/ecot⁡x dtt1+t2 is

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The value of $\int_{1 / e}^{\tan x} \frac{t}{1 + t^{2}} d t + \int_{1 / e}^{\cot x} \frac{d t}{t (1 + t^{2})}$ is