Evaluate: ∫ 1/(a^2e^x + b^2e^-x) .dx, x ∈ [-1,1]

Question

Evaluate:

\(\int_{-1}^1 \cfrac{1}{a^2e^x+b^2e^{-x}}.dx\)

∫ 1/(a²e^x + b²e^-x) .dx, x ∈ [-1,1]

Answer 1

Let \(I = \) \(\int_{-1}^1 \cfrac{1}{a^2e^x+b^2e^{-x}}.dx\)
Multiplying each term by e^x , we get