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Pertanyaan

Hasil dari integral fraction numerator 3 x squared minus 8 x plus 7 over denominator open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses cubed end fraction blank straight d x adalah ….

  1. 1 over open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses squared plus C  

  2. negative 1 over open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses squared plus C  

  3. negative fraction numerator 1 over denominator 2 open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses cubed end fraction plus C  

  4. fraction numerator 1 over denominator 2 open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses squared end fraction plus C  

  5. negative fraction numerator 1 over denominator 2 open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses squared end fraction plus C  

M. Haidar.

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Dari soal diberikan integral aljabar sebagai berikut.

integral fraction numerator 3 x squared minus 8 x plus 7 over denominator open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses cubed end fraction blank straight d x

Jika x cubed minus 4 x squared plus 7 x minus 15 equals u, maka didapat perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals cell 3 x squared minus 8 x plus 7 end cell row cell integral open parentheses fraction numerator straight d u over denominator straight d x end fraction close parentheses straight d x end cell equals cell integral open parentheses 3 x squared minus 8 x plus 7 close parentheses straight d x end cell row cell integral straight d u end cell equals cell integral open parentheses 3 x squared minus 8 x plus 7 close parentheses straight d x end cell end table 

Kemudian, perhatikan bahwa

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 3 x squared minus 8 x plus 7 over denominator open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses cubed end fraction blank straight d x end cell equals cell integral 1 over u cubed blank straight d u end cell row blank equals cell integral u to the power of negative 3 end exponent blank straight d u end cell row blank equals cell negative 1 half u to the power of negative 2 end exponent plus C end cell row blank equals cell negative fraction numerator 1 over denominator 2 u squared end fraction plus C end cell end table 

Ingat kembali bahwa u equals x cubed minus 4 x squared plus 7 x minus 15 sehingga diperoleh hasil sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 3 x squared minus 8 x plus 7 over denominator open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses cubed end fraction blank straight d x end cell equals cell negative fraction numerator 1 over denominator 2 u squared end fraction plus C end cell row blank equals cell negative fraction numerator 1 over denominator 2 open parentheses x cubed minus 4 x squared plus 7 x minus 15 close parentheses squared end fraction plus C end cell end table 

Jadi, jawaban yang tepat adalah E.

44

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