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Hasil ∫ ( x 2 + 2 ) ( x 3 + 6 x + 1 ) 2 1 ​ d x = ...

Hasil  = ...

  1. begin mathsize 12px style 2 over 9 open parentheses x cubed plus 6 x plus 1 close parentheses square root of x cubed plus 6 x plus 1 end root plus C end style

  2. begin mathsize 12px style 1 third open parentheses x cubed plus 6 x plus 1 close parentheses square root of x cubed plus 6 x plus 1 end root plus C end style

  3. begin mathsize 12px style 1 half open parentheses x cubed plus 6 x plus 1 close parentheses square root of x cubed plus 6 x plus 1 end root plus C end style

  4. begin mathsize 12px style 2 over 3 open parentheses x cubed plus 6 x plus 1 close parentheses square root of x cubed plus 6 x plus 1 end root plus C end style

  5. begin mathsize 12px style 3 over 2 open parentheses x cubed plus 6 x plus 1 close parentheses square root of x cubed plus 6 x plus 1 end root plus C end style

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Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Misal: Jadi,

begin mathsize 12px style integral f open parentheses g open parentheses x close parentheses close parentheses times g to the power of 1 open parentheses x close parentheses d x equals integral f open parentheses u close parentheses d u equals F left parenthesis u right parenthesis plus C equals F open parentheses g open parentheses x close parentheses close parentheses plus C  integral open parentheses x squared plus 2 close parentheses open parentheses x cubed plus 6 x plus 1 close parentheses to the power of begin inline style 1 half end style end exponent d x end style

Misal:

begin mathsize 12px style u left parenthesis x right parenthesis equals x cubed plus 6 x plus 1  left right double arrow d u equals open parentheses 3 x squared plus 6 close parentheses d x  left right double arrow d u equals 3 open parentheses x squared plus 2 close parentheses d x  left right double arrow 1 third d u equals open parentheses x squared plus 2 close parentheses d x  integral open parentheses x squared plus 2 close parentheses open parentheses x cubed plus 6 x plus 1 close parentheses to the power of begin inline style 1 half end style end exponent d x  equals 1 third integral u to the power of begin inline style 1 half end style end exponent d u  equals 1 third times 2 over 3 u to the power of begin inline style 3 over 2 end style end exponent plus C  equals 2 over 9 u times u to the power of begin inline style 1 half end style end exponent equals C  equals 2 over 9 open parentheses x cubed plus 6 x plus 1 close parentheses square root of x cubed plus 6 x plus 1 end root plus C  end style

Jadi, 

begin mathsize 12px style integral open parentheses x squared plus 2 close parentheses open parentheses x cubed plus 6 x plus 1 close parentheses to the power of begin inline style 1 half end style end exponent d x  equals 2 over 9 open parentheses x cubed plus 6 x plus 1 close parentheses square root of x cubed plus 6 x plus 1 end root plus C end style

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