Tentukanlah ∫4^(x^2 ) xdx

Posted by andi telaumbanua on Jul 29, 2018 in Matematika |
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Tentukanlah ∫4^(x^2 ) xdx

Jawab:

Misalkan:
u= x^2
dx = du/2x

Maka:
∫4^(x^2 ) xdx= ∫4^u x(du/2x)
=1/2 ∫4^u du

Karena : 4^u=e^uln4

maka:
=1/2 ∫e^uln4 du

Misalkan:
a = u ln 4
du = da/(ln 4)

Sehingga:
=1/2 ∫e^a (da/(ln 4))
= 1/(2 ln4) ∫e^a da
= e^a/(2 ln4)

Karena a = u ln 4 maka

= e^(u ln4)/(2 ln4)

Karena u= x^2 maka:

= e^(x^2 ln4)/(2 ln4)

Karena e^(x^2 ln4)=4^(x^2 ) maka

= 4^(x^2 )/(2 ln4)

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