Pertanyaan

Hasil dari ∫ 6 x − x 3 x 2 − 2 d x = ....

Hasil dari $\int \frac{x ^{2} - 2}{6 x - x ^{3}} d x$ = ....

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Klaim

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style Misal colon space straight u equals 6 straight x minus straight x cubed d u equals 6 minus 3 straight x squared space dx du equals negative 3 open parentheses straight x squared minus 2 close parentheses dx minus 1 third du equals open parentheses straight x squared minus 2 close parentheses dx integral space fraction numerator straight x squared minus 2 over denominator square root of 6 straight x minus straight x cubed end root end fraction dx equals integral fraction numerator 1 over denominator square root of straight u end fraction straight space. straight space open parentheses negative 1 third close parentheses du equals negative 1 third integral straight u to the power of negative 1 half end exponent du equals negative 1 third straight space. straight space 2 straight u to the power of 1 half end exponent plus straight C equals negative 2 over 3 square root of straight u plus straight C equals negative 2 over 3 square root of 6 straight x minus straight x cubed end root plus straight C end style$