(a) ∫ (2x+10)dx (b)∫ √(8+5x) dx (c)∫ dx /(3x+1)^2

Posted by andi telaumbanua on Feb 17, 2018 in Matematika |
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Hitunglah integral berikut:

  1. ∫ (2x+10)dx

  2. ∫ √(8+5x) dx

  3. ∫ dx /(3x+1)^2

Jawab:

1.∫ (2x+10) dx = 2/(1+1) x^(1+1)+ 10x+C =  x^2+ 10x+C

2. Misalkan : u = 8 + 5x

Maka: du/dx=5 Sehingga: dx = 1/5 du

∫ √(8+5x) dx = ∫ (u)^(1/2) 1/5 du = 1/5 ∫ (u)^(1/2) du = (1/5) 1/(1/2+ 1) u^(1/2+1)+ C =  (1/5) 2/3 u^(3/2)+ C = 2/15 (8+5x)^(3/2)+ C= 2/15 (8+5x) √(8+5x)+C

3. Misalkan: u = 3x+1

Maka: du/dx=3 Sehingga : dx = du/3

∫ dx /(3x+1)^2 = ∫ (du/3) /(u)^2 = 1/3 ∫ du /(u)^2 =  1/3 1/(-2+1) (u)^(-2+1) +C = 1 /(-3) u^(-1) + C =  1 / (-3) (3x+1)^(-1) + C = (-1) /(9x+3) +  C

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Hitunglah integral berikut:

1. ∫ (2x+10)dx

2. ∫ √(8+5x) dx

3. ∫ dx /(3x+1)^2

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