Evaluate the following indefinite integrals.

Question

i.du/u²
ii. 6dv/v⅝

Answer 1

In both case apply the Power Rule:

∫ xⁿ dx = ( x ⁿ ⁺ ¹ ) / ( n +1 ) + C

∫ du / u²

∫ du / u² = ∫ u ⁻² ∙ du= ( u ⁻² ⁺ ¹ ) / ( - 2 +1 ) + C =

u ⁻¹ / ( - 1 ) + C = - 1 / u + C

∫ 6 dv / v⅝ = 6 ∫ dv / v⅝ = 6 ∫ v ⁻ ⅝ dv = 6 v ⁻ ⅝ ⁺ ¹ / ( - 5 / 8 + 1 ) + C =

6 v ⅜ / ( 3 / 8 ) + C = 6 ∙ 8 ∙ v ⅜ / 3 + C = 3 ∙ 2 ∙ 8 ∙ v ⅜ / 3 + C =

2 ∙ 8 ∙ v ⅜ + C = 16 ∙ v ⅜ + C