Hitung ∫(x^3+ 1)^10 x^5 dx

Posted by andi telaumbanua on Jul 28, 2018 in Matematika |
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1. Hitung ∫(x^3+ 1)^10 x^5  dx

Jawab:

Mis:

a = x^3+ 1

 x^3 = a-1

maka:

da/dx = 3x^2
dx = da/3x^2

sehingga:

∫(x^3+ 1)^10 x^5 dx = ∫(a)^10 x^5 da/3x^(2 )

= 1/3 ∫(a)^10 x^3 da

karena  x^3 = a-1 maka

= 1/3 ∫(a)^10 (a-1) da

= 1/3 ∫a^11- a^10) da

= 1/3 ( 1/12 a^12 – 1/11 a^11 ) + C

= 1/36 a^12 – 1/33 a^11 + C

= 1/36 (x^3+ 1)^12 – 1/33 (x^3+ 1)^11 + C

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