For calculus lovers

Calculus Level 4

If \(\displaystyle{f(x)~ =~ \sqrt [ 3 ]{ 1+x^2 } }\)

And \(\displaystyle{g(t)~ =~ \int _{ 0 }^{ t }{ f(x)dx }}\)

Then find the value of \(\displaystyle{\int _{ \ln\left( \tan\left( \frac { \pi }{ 6 } \right) \right) }^{ \ln\left(\tan\left( \frac { \pi }{ 3 } \right) \right) }{ g(x)dx } }\).

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