Evaluate $\int _ { 0 } ^ { \infty } \frac { x } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x$
A) $1 / 2$
B) $1 / 4$
C) 1/8
D) 0

Name: Evaluate $\int _ { 0 } ^ { \infty } \frac { x } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x$ A) $1 / 2$ B) $1 / 4$ C) 1/8 D) 0
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The integral can be solved using a trigonometric substitution or recognizing it as a standard form. Using the substitution $x = 2\tan(\theta)$, the integral simplifies and evaluates to $1/8$.

Evaluate ∫0∞x(x2+4)2dx\int _ { 0 } ^ { \infty } \frac { x } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x∫0∞​(x2+4)2x​dx

Evaluate $\int _ { 0 } ^ { \infty } \frac { x } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x$