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Hasil dari begin mathsize 14px style blank integral 2 x open vertical bar x close vertical bar left parenthesis 8 x squared plus 3 right parenthesis square root of 4 x squared plus 3 end root d x end style adalah ...

  1. begin mathsize 14px style 2 over 3 times open parentheses 4 x to the power of 4 plus 3 x squared close parentheses to the power of 3 over 2 end exponent plus C end style

  2. begin mathsize 14px style 2 over 3 times open parentheses 4 x to the power of 4 minus 3 x squared close parentheses to the power of 3 over 2 end exponent plus C end style

  3. begin mathsize 14px style negative 2 over 3 times open parentheses 4 x to the power of 4 plus 3 x squared close parentheses to the power of 3 over 2 end exponent plus C end style

  4. begin mathsize 14px style 3 over 2 times open parentheses 4 x to the power of 4 plus 3 x squared close parentheses to the power of 3 over 2 end exponent plus C end style

  5. begin mathsize 14px style negative 3 over 2 times open parentheses 4 x to the power of 4 plus 3 x squared close parentheses to the power of 3 over 2 end exponent plus C end style

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H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Ingat bahwa Kemudian, perhatikan perhitungan berikut Jika dimisalkan , maka didapat Sehingga, kita peroleh hasil sebagai berikut

Ingat bahwa begin mathsize 14px style open vertical bar x close vertical bar equals square root of x squared end root. end style Kemudian, perhatikan perhitungan berikut

begin mathsize 14px style integral 2 x open vertical bar x close vertical bar left parenthesis 8 x squared plus 3 right parenthesis square root of 4 x squared plus 3 end root d x equals integral 2 x times open parentheses square root of x squared end root close parentheses times left parenthesis 8 x squared plus 3 right parenthesis square root of 4 x squared plus 3 end root d x equals integral 2 x times left parenthesis 8 x squared plus 3 right parenthesis square root of open parentheses x squared close parentheses times left parenthesis 4 x squared plus 3 right parenthesis end root d x equals integral open parentheses 16 x cubed plus 6 x close parentheses square root of 4 x to the power of 4 plus 3 x squared end root d x end style

Jika dimisalkan begin mathsize 14px style 4 x to the power of 4 plus 3 x squared equals u end style, maka didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d u over denominator d x end fraction end cell equals cell 16 x cubed plus 6 x end cell row cell integral open parentheses fraction numerator d u over denominator d x end fraction close parentheses d x end cell equals cell integral left parenthesis 16 x cubed plus 6 x right parenthesis d x end cell row cell integral d u end cell equals cell integral left parenthesis 16 x cubed plus 6 x right parenthesis d x end cell end table end style

Sehingga, kita peroleh hasil sebagai berikut

begin mathsize 14px style integral open parentheses 16 x cubed plus 6 x close parentheses square root of 4 x to the power of 4 plus 3 x squared end root d x equals integral square root of u d u equals 2 over 3 times u to the power of 3 over 2 end exponent plus C equals 2 over 3 times open parentheses 4 x to the power of 4 plus 3 x squared close parentheses to the power of 3 over 2 end exponent plus C end style

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