On the convergence of the anomalous integral of the flaw point type

On the convergence of the anomalous integrals of the point-of-leisure

@ (Calculus)

Integral upper and lower bounds to determine the integral, in the upper and lower bounds of the existence of a spare point, what should be done more easily to analyze whether the convergence is a very interesting problem.
An effective solution to the non-proof conclusion is to assume that f (a) tends to infinity on (A, b). The integral ∫baf (x) dx \INT_A^BF (x) dx is convergent.

The method is:
Determine if Limx→a+f (x) (x−a) δ exists, where δ∈ (0,1) determines whether \lim_{x\rightarrow a^+}f (x) (x-a) ^\delta exists, where \delta \in (0,1)

Like what:

(10-3) M,n is a positive integer, an anomalous integral:

Convergence of ∫10LN2 (1−x) √mx√ndx \int_0^1\frac{\sqrt[m]{ln^2 (1-x)}}{\sqrt[n]{x}}dx (D)
A. Only M-related
B. only relevant to n
C. Related to the value of M,n
D. Regardless of the value of M,n

Analysis: If you give the object of comparison directly, as many analytic said, it will make people feel incredible, how to think of.

Here the integrand happens to be unbounded at two boundaries.

And if you follow the above idea, the problem is:

Judge:

LIMX→0+LN2 (1−x) ‾‾‾‾‾‾‾‾‾‾√mx√n (x−0) δ,δ∈ (0,1) =limx→0+