Pertanyaan

Hasil dari ∫ ( 9 x 2 − 6 x + 12 ) 3 ( 6 x − 2 ) d x = ...

Hasil dari $\int \frac{( 6 x - 2 )}{( 9 x ^{2} - 6 x + 12 ) ^{3}} d x = ...$

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Dengan menggunakan konsep integral tak tentu, maka misalkan: Selanjutnya, Jadi,

Dengan menggunakan konsep integral tak tentu, maka misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 9 x squared minus 6 x plus 12 end cell row cell d u end cell equals cell 18 x minus 6 space end cell end table

Selanjutnya,

6 x minus 2 d x equals 1 third d u

Jadi,

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator left parenthesis 6 x minus 2 right parenthesis over denominator left parenthesis 9 x squared minus 6 x plus 12 right parenthesis cubed end fraction d x end cell equals cell integral left parenthesis 6 x minus 2 right parenthesis left parenthesis 9 x squared minus 6 x plus 12 right parenthesis to the power of negative 3 end exponent d x end cell row blank equals cell integral 1 third u to the power of negative 3 end exponent d u end cell row blank equals cell fraction numerator 1 over denominator 3 cross times left parenthesis negative 2 right parenthesis end fraction u to the power of negative 2 end exponent plus c end cell row blank equals cell fraction numerator 1 over denominator negative 6 end fraction u to the power of negative 2 end exponent plus c end cell row blank equals cell fraction numerator 1 over denominator negative 6 end fraction open parentheses 9 x squared minus 6 x plus 12 close parentheses to the power of negative 2 end exponent plus c end cell end table$

Latihan Bab

Pengenalan Integral

Integral Tak Tentu

Integral Substitusi

Aplikasi Integral Tak Tentu