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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 62

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Answer:\log |(1+\log x)| + c

Hints: You must know about the rules of integration of trigonometric and inverse trigonometric functions.

Given: \int \frac{1}{x(1+\log x)} d x \\


\begin{aligned} &\int \frac{1}{x(1+\log x)} d x \\ &\operatorname{Put}(1+\log x)=t \\ &\frac{1}{x} d x=d t \\ &\int \frac{1}{x(1+\log x)} d x=\int \frac{d t}{t} \\ &=\log |t|+c \\ &\therefore=\log |(1+\log x)|+c \end{aligned}

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