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Hasil dari ∫x2−2x​(x−1)​dx = ....

Pertanyaan

Hasil space dari space integral fraction numerator left parenthesis x minus 1 right parenthesis over denominator square root of x squared minus 2 x end root end fraction d x space equals space....

  1. 1 half square root of x squared minus 2 x end root space plus space straight C

  2. square root of x squared minus 2 x end root space plus space straight C

  3. 2 square root of x squared minus 2 x end root space plus space straight C

  4. 2 x square root of x squared minus 2 x end root space plus space straight C

  5. 4 x square root of x squared minus 2 x end root space plus space straight C

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

u space equals space x squared space minus space 2 x  fraction numerator d u over denominator d x end fraction equals 2 x space minus space 2 space space rightwards double arrow space space d x space equals space fraction numerator d u over denominator 2 x minus 2 end fraction    integral fraction numerator x minus 1 over denominator square root of x squared space minus space 2 x end root end fraction d x space equals space integral fraction numerator x minus 1 over denominator square root of u end fraction space fraction numerator d u over denominator 2 x minus 2 end fraction space equals space integral fraction numerator 1 over denominator 2 square root of u end fraction d u space equals space integral 1 half u to the power of negative 1 half end exponent d u space equals space u to the power of 1 half end exponent plus C space equals space square root of x squared minus 2 x end root space plus space C

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