Hasil dari ∫6x2(x3+2)2 dx adalah ...

Pertanyaan

Hasil dari $\int6x^2\left(x^3+2\right)^2\;\mathrm dx$ adalah ...

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

hasil dari integral 6 x squared open parentheses x cubed plus 2 close parentheses squared space straight d x

adalah

Pembahasan

integral 6 x squared open parentheses x cubed plus 2 close parentheses squared space straight d x

Misal

$table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x cubed plus 2 end cell row cell straight d u end cell equals cell 3 x squared space straight d x end cell row cell d x end cell equals cell fraction numerator d u over denominator 3 x squared end fraction end cell end table$

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral 6 x squared open parentheses x cubed plus 2 close parentheses squared space straight d x end cell equals cell integral space stack up diagonal strike 6 x squared end strike with 2 on top times u squared space fraction numerator d u over denominator up diagonal strike 3 x squared end strike end fraction end cell row blank equals cell integral space 2 u squared space d u end cell row blank equals cell 2 over 3 u cubed plus C end cell row blank equals cell 2 over 3 open parentheses x cubed plus 2 close parentheses cubed plus C end cell end table$

Jadi, hasil dari integral 6 x squared open parentheses x cubed plus 2 close parentheses squared space straight d x adalah