Find the Value of the Integral $\int _ { 0 } ^ { 1 } \frac { x ^ { 2 } } { \left( x ^ { 3 } + 1 \right) ^ { 2 } } d x$

Find the value of the integral $\int _ { 0 } ^ { 1 } \frac { x ^ { 2 } } { \left( x ^ { 3 } + 1 \right) ^ { 2 } } d x$

A) $\frac { 3 } { 4 }$
B) 2
C) $\frac { 3 } { 7 }$
D)
$\frac { 7 } { 3 }$
E) $\frac { 1 } { 6 }$
F) $\frac { 3 } { 2 }$
G) $\frac { 2 } { 3 }$
H) 1

Correct Answer:

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