Pertanyaan

Hasil dari ∫ x 2 − 3 x − 5 6 x − 9 d x adalah ....

Hasil dari $\int \frac{6 x - 9}{x ^{2} - 3 x - 5} d x$ adalah ....

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style Misal colon straight u equals straight x squared minus 3 straight x minus 5 du equals 2 straight x minus 3 space dx du equals left parenthesis 2 straight x minus 3 right parenthesis dx space 3 space du equals left parenthesis 6 straight x minus 9 right parenthesis dx integral fraction numerator 6 straight x minus 9 over denominator square root of straight x squared minus 3 straight x minus 5 end root end fraction straight space dx equals integral fraction numerator 1 over denominator square root of straight u end fraction straight space. straight space 3 space du equals integral 3 straight u to the power of negative 1 half end exponent du equals fraction numerator 3 over denominator 1 half end fraction straight u to the power of 1 half end exponent plus straight C equals 6 square root of straight u plus straight C equals 6 square root of straight x squared minus 3 straight x minus 5 end root plus straight C end style$