hasil dari \int2^0 x akar 2x+1 dx ......??

jawab

₀²∫ x√(2x + 1) dx

u = 2x + 1
2x  = u - 1
x = 1/2 (u -1)
x = (1/2 u - 1/2)

batas integral
u = 2x +1
x = 0 -->  u = 1
x = 2 --> u = 5

₁⁵∫ (1/2 u - 1/2)(u)^(1/2) du

= ₁⁵ ∫ 1/2 u^(3/2) - 1/2 u^(1/2) du

= [1/2 (2/5) u^(5/2)  - 1/2 (2/3)u^(3/2) ]⁵₁

= 1/5 u²√u  - 1/3 u√u ]⁵₁

= 1/5 (25√5 - 1) - 1/3 (5√5 -1)
= 5√5 - 1/5 - 5/3 √5 + 1/3
= 10/3 √5 + 2/15
= 2/15 (25√5 + 2)