Reverse the Order of Integration and Then Evaluate the Integral $\int _ { 0 } ^ { 512 } \int _ { \sqrt [ 3 ] { x } } ^ { 8 } \frac { 1 } { y ^ { 4 } + 1 } d y d x$

Multiple Choice

Reverse the order of integration and then evaluate the integral.
- $\int _ { 0 } ^ { 512 } \int _ { \sqrt [ 3 ] { x } } ^ { 8 } \frac { 1 } { y ^ { 4 } + 1 } d y d x$

A) $\frac { \ln 4097 - 1 } { 4 }$
B) $\ln 8 - 1$
C) $\frac { \ln 4097 } { 4 }$
D) $\ln 8$