Pertanyaan

Hasil ∫ x 3 + 6 x + 1 x 2 + 2 d x = ....

Hasil $\int \frac{x ^{2} + 2}{x ^{3} + 6 x + 1} d x$ = ....

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

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