Evaluate the improper integral or state that it is divergent.
-$$\int _ { 1 } ^ { \infty } \frac { 14 } { 8 x ( x + 1 ) ^ { 2 } } d x$$
A) Divergent
B) -1.569
C) 0.337
D) 1.569

Question

Quizplus · Accepted Answer

To evaluate the improper integral $\int _ { 1 } ^ { \infty } \frac { 14 } { 8 x ( x + 1 ) ^ { 2 } } d x$, we first perform partial fraction decomposition. The integral simplifies to a form that can be integrated using standard calculus techniques. After integrating and applying the limits from 1 to infinity, the result converges to a finite value, indicating that the integral is not divergent. The correct computation leads to the value 0.337, making option C the correct answer.

Evaluate the Improper Integral or State That It Is Divergent ∫1∞148x(x+1)2dx\int _ { 1 } ^ { \infty } \frac { 14 } { 8 x ( x + 1 ) ^ { 2 } } d x∫1∞​8x(x+1)214​dx

Evaluate the Improper Integral or State That It Is Divergent $\int _ { 1 } ^ { \infty } \frac { 14 } { 8 x ( x + 1 ) ^ { 2 } } d x$