D E W I: Integral Substitusi 2

Nur Dewi

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Contoh 2 :
$\int x\left ( x^{2}+8 \right )^{19}dx = ...$

Jawab :
Misal y = x² + 8
maka
$\frac{dy}{dx}=2x$
Sehingga
$dx=\frac{dy}{2x}$

Maka
$\int x\left ( x^{2}+8 \right )^{19}dx = \int xy^{19}\frac{dy}{2x}=\frac{1}{2}\int y^{19}dy$
$= \frac{1}{2}.\frac{1}{20}y^{20} + c = \frac{1}{40}\left ( x^{2} + 8 \right )^{20} + c$

Contoh 3 :
$\int x^{3}\left ( x^{4} - 12 \right )^{24} dx = ...$

Jawab :
misal y = x⁴ - 12
maka
$\frac{dy}{dx}= 4x^{3}$
Akibatnya
$dx=\frac{dy}{4x^{3}}$
jadi

$\int x^{3}\left ( x^{4}-12 \right )^{24}dx = \int x^{3}y^{24}\frac{dy}{4x^{3}}=\frac{1}{4}\int y^{24}dy$
$\frac{1}{4}.\frac{1}{25}y^{25}+ c = \frac{1}{100}\left ( x^{4} - 12 \right ) + c$

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Label: Integral, Substitusi

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