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Hasil dari ∫ ( x − 3 ) ( 3 x + 5 ) 3 x 4 − 16 x 3 + 10 x 2 + 48 x − 45 ​ d x adalah ....

Hasil dari  adalah ....

  1. begin mathsize 14px style 1 third x cubed plus 4 over 2 x squared plus 3 x plus C end style 

  2. begin mathsize 14px style 1 third x cubed minus 4 over 2 x squared minus 3 x plus C end style 

  3. begin mathsize 14px style 1 third x cubed minus 4 over 2 x squared plus 3 x plus C end style 

  4. begin mathsize 14px style 1 third x to the power of 4 minus 4 over 2 x squared plus 3 x plus C end style 

  5. begin mathsize 14px style 1 third x to the power of 4 plus 4 over 2 x squared minus 3 x plus C end style 

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H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

jawaban yang tepat adalah C.

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Pembahasan

Perhatikan perhitungan berikut. Misalkan maka Jadi, jawaban yang tepat adalah C.

Perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 3 x to the power of 4 minus 16 x cubed plus 10 x squared plus 48 x minus 45 over denominator left parenthesis x minus 3 right parenthesis left parenthesis 3 x plus 5 right parenthesis end fraction blank d x end cell equals cell integral fraction numerator open parentheses x minus 3 close parentheses open parentheses 3 x plus 5 close parentheses open parentheses x squared minus 4 x plus 3 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses 3 x plus 5 close parentheses end fraction blank d x end cell row blank equals cell integral open parentheses x squared minus 4 x plus 3 close parentheses blank d x end cell row blank equals cell integral x squared blank d x minus 4 integral x blank d x plus integral 3 blank d x end cell row blank equals cell open parentheses fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus C subscript 1 close parentheses minus 4 open parentheses fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus C subscript 2 close parentheses plus open parentheses 3 x plus C subscript 3 close parentheses end cell row blank equals cell 1 third x cubed minus 4 over 2 x squared plus 3 x plus C subscript 1 minus 4 C subscript 2 plus C subscript 3 end cell end table end style 

Misalkan begin mathsize 14px style C subscript 1 minus 4 C subscript 2 plus C subscript 3 equals C comma end style maka

begin mathsize 14px style 1 third x cubed minus 4 over 2 x squared plus 3 x plus C subscript 1 minus 4 C subscript 2 plus C subscript 3 equals 1 third x cubed minus 4 over 2 x squared plus 3 x plus C end style 

Jadi, jawaban yang tepat adalah C.

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