Evaluate the improper integral: $\int _ { 3 } ^ { \infty } \frac { x ^ { 2 } } { \left( x ^ { 3 } + 3 \right) ^ { 2 } } d x$
A) $\frac { 1 } { 60 }$
B) $\frac { 1 } { 90 }$
C) 90
D) $\frac { 1 } { 92 }$

Name: Evaluate the improper integral: $\int _ { 3 } ^ { \infty } \frac { x ^ { 2 } } { \left( x ^ { 3 } + 3 \right) ^ { 2 } } d x$ A) $\frac { 1 } { 60 }$ B) $\frac { 1 } { 90 }$ C) 90 D) $\frac { 1 } { 92 }$
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Question

Quizplus · Accepted Answer

The integral converges and evaluates to $\frac{1}{90}$ using substitution and limits.

Evaluate the Improper Integral ∫3∞x2(x3+3)2dx\int _ { 3 } ^ { \infty } \frac { x ^ { 2 } } { \left( x ^ { 3 } + 3 \right) ^ { 2 } } d x∫3∞​(x3+3)2x2​dx

Evaluate the Improper Integral $\int _ { 3 } ^ { \infty } \frac { x ^ { 2 } } { \left( x ^ { 3 } + 3 \right) ^ { 2 } } d x$