Level:
Project ID:
1003107912
Accepted:
1
Which method is the most effective to solve the indefinite integral
\[ \int\frac{\mathrm{d}x}{x\ln x} \]
in the range \( (1;\infty) \)?
By substitution, \( a=\ln x \).
By parts integration, when we let \( u(x)=\frac1x \), where \( u(x) \) is the integrated function, and we let \( v'(x)=\ln x \), where \( v'(x) \) is the differentiated function.
By substitution, \( a=\frac1x \).
By factorization into \( \int\frac1x\mathrm{d}x\cdot\int\frac1{\ln x}\mathrm{d}x \).