"I am back" says Integration

Calculus Level 4

\[ \large \int \dfrac{e^{3x} + e^x}{e^{4x} - e^{2x} + 1} \, dx \]

If the value of the indefinite integral above can be written as \[ \arctan(ae^{bx} - ge^{dx} ) + C , \] where \(a,b,d\) and \(g\) are constant integers, find \(101(a^2+b + d^3 + g^4) \).

Clarification: \(C\) denotes the arbitrary constant of integration.

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