Integral dari : (a) ∫ ctg x dx (b) ∫ (x dx) /(1- x^2 )

Posted by andi telaumbanua on Feb 17, 2018 in Matematika |
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Tentukanlah Integral dari :

  1. ∫ ctg x dx

  2. ∫ (x dx) /(1- x^2 )

Jawab:

1. ctg x = cos⁡x/sin⁡x

misalkan: u = sin x

maka: du/dx= cos⁡x

Sehingga: dx = du/cos⁡x

∫ctg x dx = ∫ cos⁡x / sin⁡x dx = ∫( cos⁡x /u) ( du/cos⁡x) = ∫ du / u = ln⁡|u| + C = ln⁡| sin⁡x | + C

2. misalkan: u = 1- x^2

maka: du/dx = -2x

Sehingga: dx = du /(-2x)

∫ (x dx) /(1- x^2 ) = ∫ (x/u) [du /(-2x)] = 1 /(-2) ∫ du /u = 1/(-2)  ln⁡ |u| + C = 1/(-2) ln⁡ |1- x^2 | +  C

 

 

 

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Tentukanlah Integral dari :

1. ∫ ctg x dx

2. ∫ (x dx)/(1- x^2)

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