integral http://192.168.1.6/content/images/921.PNG

Kode : 12.2.1 [Kelas 12 Matematika BAB 1 - Integral]

Pembahasan

[tex] \int\ { \frac{x^3}{(x^4-3)^6} } \, dx [/tex]

Metoda substitusi

u = x⁴ - 3
 [tex] \frac{du}{dx}=4x^3 [/tex]
[tex]dx= \frac{du}{4x^3} [/tex]

[tex]= \int\ {(x^3)(x^4-3)^{-6}} } \, dx[/tex]
[tex]= \int\ {(x^3)u^{-6}} } \, \frac{du}{4x^3} [/tex]
[tex]= \frac{1}{4} \int\ u^{-6}} } \, du[/tex]
[tex]=(\frac{1}{4}) (\frac{1}{-5})u^{-5}} } +c[/tex]
[tex]=-\frac{1}{20}u^{-5}} } +c[/tex]
[tex]=- \frac{1}{20}(x^4-3)^{-5}+c [/tex]
[tex]=- \frac{1}{20(x^4-3)^{5}}+c [/tex]