Pertanyaan

∫ ( 3 x − 1 ) 9 d x ...

$\int (3 x - 1)^{9} d x$ ...

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh

Pembahasan

Dengan konsep substitusi integral, didapat: Misalkan: Sehingga, Dengan demikian, diperoleh .

Dengan konsep substitusi integral, didapat:

Misalkan:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 3 x minus 1 end cell row cell fraction numerator d u over denominator d x end fraction end cell equals 3 row cell d u end cell equals cell 3 d x end cell row cell d x end cell equals cell 1 third d u end cell end table end style$

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 3 x minus 1 close parentheses to the power of 9 d x end cell equals cell integral u to the power of 9 over 3 d u end cell row blank equals cell 1 third times integral thin space u to the power of 9 d u end cell row blank equals cell 1 third times fraction numerator u to the power of 9 plus 1 end exponent over denominator 9 plus 1 end fraction plus C end cell row blank equals cell 1 third times fraction numerator open parentheses 3 x minus 1 close parentheses to the power of 9 plus 1 end exponent over denominator 9 plus 1 end fraction plus C end cell row blank equals cell 1 third times open parentheses 3 x minus 1 close parentheses to the power of 10 over 10 plus C end cell row blank equals cell 1 over 30 open parentheses 3 x minus 1 close parentheses to the power of 10 plus C end cell end table end style$

Dengan demikian, diperoleh .