Question

Let I = ∫ (e^x/(e^4x + e^2x + 1)) dx, 

J = (e^–x/(e^–4x + e^–2x + 1)) dx. 

For an arbitrary constant C, the value of J – I is 

(a) (1/2) log (e^4x – e^2x + 1/(e^4x + e^x + 1)) + c 

(b) (1/2) log (e^2x + e^x + 1/(e^2x – e^x + 1)) + c 

(c) (1/2) log (e^2x – e^x + 1/(e^2x + e^x + 1)) + c 

(d) (1/2) log (e^4x + e^2x + 1/(e^4x – e^2x + 1)) + c

Answer 1

Correct option is (b)

Explanation : 

J – I 

Let e^x = t 

e^x dx = dt