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∫ 9 x 2 x 3 − 1 ​ d x = …

  1. 1 fourth open parentheses x cubed minus 1 close parentheses square root of x cubed minus 1 end root plus c

  2. 1 half open parentheses x cubed minus 1 close parentheses square root of x cubed minus 1 end root plus c

  3. open parentheses x cubed minus 1 close parentheses square root of x cubed minus 1 end root plus c

  4. 2 open parentheses x cubed minus 1 close parentheses square root of x cubed minus 1 end root plus c

  5. 4 open parentheses x cubed minus 1 close parentheses square root of x cubed minus 1 end root plus c

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M. Nizar

Master Teacher

Mahasiswa/Alumni Universitas Siliwangi

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Pembahasan

M i s a l k a n colon u equals x cubed minus 1 fraction numerator d u over denominator d x end fraction equals 3 x squared d x equals fraction numerator d u over denominator 3 x squared end fraction  integral 9 x squared space square root of x cubed minus 1 end root d x space equals integral 9 x squared space square root of u space fraction numerator d u over denominator 3 x squared end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals integral 3 u to the power of 1 half end exponent d u space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 over denominator 3 over 2 end fraction u to the power of 3 over 2 end exponent plus c space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 u square root of u plus c space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 open parentheses x cubed minus 1 close parentheses square root of x cubed minus 1 end root plus c

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integral fraction numerator 6 x minus 2 over denominator open parentheses 3 x squared minus 2 x plus 1 close parentheses cubed end fraction d x equals horizontal ellipsis

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