integral dari : (a) ∫x e^( x^2 ) dx (b)∫ dx/(x ln⁡x ) (c) ∫ (e^x dx)/(1+2e^x )

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

  1. ∫x e^( x^2 ) dx

  2. ∫ dx/(x ln⁡x )

  3. ∫ (e^x dx)/(1+2e^x )

 

Jawab:

1. Misalkan: u = x^2

Maka: du/dx = 2x

Sehingga : dx = du/2x

∫ x e^( x^2 ) dx = ∫ x e^u  du/2x = 1/2 ∫ e^u du =  1/2 e^u +  C = 1/2 e^(x^2 ) +  C

2. Misalkan: u = ln x

Maka: du/dx = 1/x

Sehingga : dx = x du

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

3. Misalkan: u =  1 + 2e^x

Maka: du/dx = 2e^x

Sehingga : dx =  du /2e^x

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

 

 

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Tentukanlah Integral dari : 1. ∫ x e^(x^2 ) dx 2. ∫dx /(x ln⁡x ) 3. ∫ (e^x dx)/(1+2e^x )

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