Tentukanlah integral dari a. ∫[e^(3/x)/x^2] dx b. ∫x^2/(x^3+2) dx

Posted by andi telaumbanua on Jul 28, 2018 in Matematika |
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Tentukanlah

a. ∫[e^(3/x)/x^2] dx
b. ∫x^2/(x^3+2) dx

Jawab:

a. Misalkan:
u = 3/x
dx = (-du x^2)/3

maka:

∫[e^(3/x)]/[x^2] dx= ∫e^u/x^2 [((-du x^2)/3)]

=-1/3 ∫e^u du

=-1/3 (e^u )

=-1/3 e^(3/x)+C

b. Misalkan:

u = x^3+2
dx = du/(3x^2 )

maka:

∫x^2/(x^3+2) dx =∫x^2/u (du/(3x^2 ))

=1/3 ∫du/u

=1/3 (ln u)+C

=1/3 ln⁡(x^3+2)+C

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