Indefinite Integration
Integration by Substitution
JEE Main 2018
Grade 12
Question:
$\int \frac{dx}{x \ln x \ln(\ln x)}$ equals:
(1) $\ln |\ln(\ln x)| + C$
(2) $\ln |\ln x| + C$
(3) $\ln(\ln x) \cdot \ln x + C$
(4) $\frac{1}{\ln(\ln x)} + C$
Step-by-Step Solution
Key Concept: Substitute $t = \ln(\ln x)$ and check that $dt = \frac{dx}{x \ln x}$, reducing the integral to the elementary form $\int \frac{dt}{t}$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)