Pertanyaan

Hasil dari ∫ x 2 − 2 x + 4 x − 1 d x adalah ....

Hasil dari $\int \frac{x - 1}{x ^{2} - 2 x + 4} d x$ adalah ....

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C

Pembahasan

Misalkan: Dengan demikian: Jadi, jawaban yang tepat adalah C

Misalkan:

$begin mathsize 14px style u equals x squared minus 2 x plus 4 left right double arrow straight d u equals open parentheses 2 x minus 2 close parentheses straight d x left right double arrow 2 left parenthesis x minus 1 right parenthesis straight d x equals straight d u left right double arrow left parenthesis x minus 1 right parenthesis straight d x equals fraction numerator straight d u over denominator 2 end fraction end style$

Dengan demikian:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator x minus 1 over denominator square root of x squared minus 2 x plus 4 end root end fraction d x end cell equals cell integral left parenthesis x minus 1 right parenthesis left parenthesis x squared minus 2 x plus 4 right parenthesis to the power of negative 1 half end exponent d x end cell row blank equals cell integral 1 half u to the power of negative 1 half end exponent d u end cell row blank equals cell 1 half u to the power of negative 1 half end exponent d u end cell row blank equals cell 1 half cross times fraction numerator u to the power of begin display style 1 half end style end exponent over denominator begin display style bevelled 1 half end style end fraction plus C end cell row blank equals cell u to the power of 1 half end exponent plus C end cell row blank equals cell square root of x squared minus 2 x plus 4 end root plus C end cell end table end style$

Jadi, jawaban yang tepat adalah C