Question

Integrate the following with respect to x.

(i) √x⁷

(ii) (x¹⁰)^1/7

Answer 1

(i) ∫√x⁷ dx = ∫(x⁷)^1/2 dx = ∫x^7/2 dx = x^{7/2 + 1}/(7/2 + 1) = x^9/2/(9/2) = (2/9)x^9/2 + c

(ii) ∫(x¹⁰)^1/7 dx = ∫x^10/7 dx = x^{10/7 + 1}/(10/7 + 1) = x^17/7/(17/7) = (7/17)x^17/7 + c