Question

Integrate the following with respect to x.

(i) 1/x⁵

(ii) x^-1

(iii) 1/x^5/2 

Answer 1

(i) ∫1/x⁵ dx = ∫x^-5 dx = x^{-5 + 1}/(-5 + 1) = x^-4/-4 = -1/4x⁴ + c

(ii) ∫x^-1 dx = ∫1/x dx = log x + c

(iii) ∫1/x^-5/2 dx = x^{-5/2 + 1}/(-5/2 + 1) = x^-3/2/(-3/2) = -2/3x^3/2 + c