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Hasil begin mathsize 14px style integral fraction numerator x squared plus 2 over denominator square root of x cubed plus 6 x plus 1 end root end fraction space d x end style = ....

  1. begin mathsize 14px style 1 third square root of x cubed plus 6 x plus 1 end root plus C end style

  2. begin mathsize 14px style 2 over 3 square root of x cubed plus 6 x plus 1 end root plus C end style

  3. begin mathsize 14px style square root of x cubed plus 6 x plus 1 end root plus C end style

  4. begin mathsize 14px style 2 square root of x cubed plus 6 x plus 1 end root plus C end style

  5. begin mathsize 14px style 3 square root of x cubed plus 6 x plus 1 end root plus C end style

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

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Pembahasan

integral fraction numerator straight x squared plus 2 over denominator square root of straight x cubed plus 6 straight x plus 1 end root end fraction dx  Misalkan  straight u equals straight x cubed plus 6 straight x plus 1  maka  du equals 3 straight x squared plus 6 space dx  1 third du equals straight x squared plus 2 space dx  Sehingga  integral fraction numerator straight x squared plus 2 over denominator square root of straight x cubed plus 6 straight x plus 1 end root end fraction dx equals integral fraction numerator 1 over denominator square root of straight u end fraction.1 third dx  equals 1 third integral straight u to the power of negative 1 half end exponent du  equals 1 third fraction numerator straight u to the power of begin display style 1 half end style end exponent over denominator begin display style 1 half end style end fraction plus straight C  equals 2 over 3 square root of straight u plus straight C  equals 2 over 3 square root of straight x cubed plus 6 straight x plus 1 end root plus straight C

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