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Please solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.4 (b) Question 8 maths textbook solution.

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Hints:-  You must know the integration rules of trigonometric functions and its limits

Given:- \int_{0}^{\infty} \frac{\log x}{1+x^{2}} d x

Solution : \int_{0}^{\infty} \frac{\log x}{1+x^{2}} d x

Using substitute x=\frac{1}{t}

We get -\int_{0}^{1} \frac{\log x}{1+x^{2}} d x=\int_{0}^{\infty} \frac{\log x}{1+x^{2}} d x

And \therefore \int_{0}^{\infty} \frac{\log x}{1+x^{2}} d x=0

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