"I am back" says Integration

Calculus Level 4

e3x+exe4xe2x+1dx \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(aebxgedx)+C, \arctan(ae^{bx} - ge^{dx} ) + C , where a,b,da,b,d and gg are constant integers, find 101(a2+b+d3+g4)101(a^2+b + d^3 + g^4) .

Clarification: CC denotes the arbitrary constant of integration.

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