Question

∫[dx/(e^x + e^–x)] = _______ + c 

(a) log|e^x + e^–x| 

(b) tan^–1(e^x) 

(c) log|e^x + 1| 

(d) tan^–1(e^–x)

Answer 1

The correct option (b) tan^–1(e^x)  

Explanation:

I = ∫[dx/(e^x + e^–x)] = ∫[e^x/(e^2x + 1)]dx 

Let e^x = t hence e^xdx = dt 

∴ I = ∫[dt/(t² + 1)] 

I = tan^–1t = tan^–1(e^x)