Question

Let f(x) = x³ ((x²/(e^{x^2} – 1)) + (x²/2) + 1)). Find the value of ∫f(x) dx for x ∈ [√(In(1/2)),√(In(2))].

Answer 1

Let

Let 

= – f(x) 

∴ f(x) is an odd function. 

The value of the given Integral is zero. 

I = 0, (∵ it is an odd function)