Evaluate the improper integral: $\int _ { 0 } ^ { \infty } \frac { 1 } { ( x - 7 ) \ln ( x - 7 ) } d x$ Round your answer to two decimal places, if necessary.
A) -inf
B) 0.00
C) 2.08
D) Undefined

Question

Quizplus · Accepted Answer

The integral is undefined because the function $ \frac { 1 } { ( x - 7 ) \ln ( x - 7 ) } $ is undefined at $x = 7$ and for $x \leq 7$, including at the lower limit of the integral. This makes the integral improper not only at infinity but also at the singularity point $x = 7$, where the function does not have a defined value.

Evaluate the Improper Integral ∫0∞1(x−7)ln⁡(x−7)dx\int _ { 0 } ^ { \infty } \frac { 1 } { ( x - 7 ) \ln ( x - 7 ) } d x∫0∞​(x−7)ln(x−7)1​dx

Evaluate the Improper Integral $\int _ { 0 } ^ { \infty } \frac { 1 } { ( x - 7 ) \ln ( x - 7 ) } d x$