Question

∫e^4logx(x⁵ + 1)^–1 = ________ + c 

(a) (1/5)log(x⁴ + 1) 

(b) – log(x⁴ + 1) 

(c) log(x⁴ + 1) 

(d) (1/5)log(x⁵ + 1)

Answer 1

The correct option (d) (1/5)log(x⁵ + 1)   

Explanation:

I = ∫e^4logx(x⁵ + 1)^–1dx = ∫[x⁴/(x⁵ + 1)]dx 

Put x⁵ + 1 = t 

∴ 5x⁴dx = dt 

∴ I = ∫(dt/t) ∙ (1/5) 

= (1/5)logt + c 

= (1/5)log(x⁵ + 1) + c