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∫ ( − 18 x 2 − 6 x + 1 ) d ( − 3 x ) = ...

  1. 54 x cubed plus 18 x squared plus 3 x plus C

  2. 27 x cubed plus 9 x squared plus 3 x plus C

  3. 18 x cubed plus 9 x squared plus 3 x plus C

  4. 18 x cubed plus 9 x squared minus 3 x plus C

  5. negative 9 x cubed minus 6 x squared minus 3 x plus C

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N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Misalkan u = -3x, maka Sehingga hasilnya adalah

integral space left parenthesis negative 18 x squared minus 6 x plus 1 right parenthesis space d left parenthesis negative 3 x right parenthesis space equals negative 2 left parenthesis negative 3 x right parenthesis squared plus 2 left parenthesis negative 3 x right parenthesis plus 1 space d left parenthesis negative 3 x right parenthesis

Misalkan u = -3x, maka

integral space left parenthesis negative 18 x squared minus 6 x plus 1 right parenthesis space d left parenthesis negative 3 x right parenthesis space equals negative 2 left parenthesis negative 3 x right parenthesis squared plus 2 left parenthesis negative 3 x right parenthesis plus 1 space d left parenthesis negative 3 x right parenthesis equals integral negative 2 u squared plus 2 u plus 1 space d u equals negative 2 over 3 u cubed plus u squared plus u space plus C

Sehingga hasilnya adalah

negative 2 over 3 u cubed plus u squared plus u space plus C space equals space minus 2 over 3 left parenthesis negative 3 x right parenthesis cubed plus left parenthesis negative 3 x right parenthesis squared plus left parenthesis negative 3 x right parenthesis plus C equals negative 2 over 3 open parentheses negative 27 x cubed close parentheses plus 9 x squared minus 3 x plus C equals 18 x cubed plus 9 x squared minus 3 x plus C

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