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∫(x41​+4x​1​) dx=...

Pertanyaan

integral open parentheses 1 over x to the power of 4 plus fraction numerator 1 over denominator fourth root of x end fraction close parentheses space d x equals... 

  1. negative fraction numerator 1 over denominator 3 x cubed end fraction plus 4 over 3 fourth root of x cubed end root plus straight C

  2. negative fraction numerator 1 over denominator 3 x cubed end fraction minus 4 over 3 fourth root of x cubed end root plus straight C

  3. fraction numerator 1 over denominator 3 x cubed end fraction minus 4 over 3 fourth root of x cubed end root plus straight C

  4. fraction numerator 1 over denominator 3 x cubed end fraction plus 4 over 3 fourth root of x cubed end root plus straight C

  5. fraction numerator 1 over denominator 3 x cubed end fraction minus 3 over 4 fourth root of x cubed end root plus straight C

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jika f left parenthesis x right parenthesis equals straight a times x to the power of straight n, maka integral f left parenthesis x right parenthesis space d x equals fraction numerator 1 over denominator straight n plus 1 end fraction times straight a times x to the power of straight n plus 1 end exponent plus straight C.


integral open parentheses 1 over x to the power of 4 plus fraction numerator 1 over denominator fourth root of x end fraction close parentheses space d x equals integral space open parentheses x to the power of negative 4 end exponent plus x to the power of negative bevelled 1 fourth end exponent close parentheses space d x equals fraction numerator 1 over denominator negative 4 plus 1 end fraction x to the power of negative 4 plus 1 end exponent plus fraction numerator 1 over denominator negative begin display style bevelled 1 fourth end style plus 1 end fraction x to the power of negative bevelled 1 fourth plus 1 end exponent plus straight C equals negative 1 third straight x to the power of negative 3 end exponent plus fraction numerator 1 over denominator begin display style bevelled 3 over 4 end style end fraction straight x to the power of bevelled 3 over 4 end exponent plus straight C equals negative fraction numerator 1 over denominator 3 straight x cubed end fraction plus 4 over 3 fourth root of straight x cubed end root plus straight C


Oleh karena itu, jawaban yang benar adalah A.

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