* ∫ (2x+10)/(3x-5) dx * ∫ √10 + 3x - 2x2 dx

jawab

u = 3x - 5 --> du = 3 dx --> dx = 1/3 du
3x= u + 5
x = 1/3 ( u + 5)
2x + 10 = 2/3 (u + 5) + 10 = 2/3 u + 10/3 + 10 
2x + 10 = 1/3 ( 2u + 40)

∫(2x + 10) / (3x - 5) dx = ∫ 1/3(2u + 40) (u)⁻¹. 1/3 du

= 1/9 ∫ 2+ 40u⁻¹ du

= 1/9 { 2u + 40 ln u} + c

= 1/9 { 2(3x-5) + 40 ln(3x-5) }+ c

= 1/9 (6x -10 + 40 ln  (3x - 5)  + c

u = 3x - 5
dx = 1/3 du
3x= u + 5
x = 1/3 ( u + 5)
2x + 10 =
= 2/3 u + 10/3 + 10
2x + 10
= 1/3 ( 2u + 40)


∫(2x + 10) / (3x - 5) dx = ∫ 1/3(2u + 40) (u)¹. 1/3 du
= 1/9 {2u + 40 ln u} + c
= 1/9 (6x -10 + 40 In (3x - 5) + c

#semogamembantu

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