Pertanyaan

H a s i l d a r i ∫ x 2 − 4 x + 5 4 x − 8 d x = ...

$H a s i l d a r i \int \frac{4 x - 8}{x ^{2} - 4 x + 5} d x = ...$

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

$u equals x squared minus 4 x plus 5 fraction numerator d u over denominator d x end fraction equals 2 x minus 4 rightwards double arrow d x equals fraction numerator d u over denominator left parenthesis 2 x minus 4 right parenthesis end fraction integral fraction numerator left parenthesis 4 x minus 8 right parenthesis over denominator square root of x squared minus 4 x plus 5 end root end fraction d x equals integral fraction numerator left parenthesis 4 x minus 8 right parenthesis over denominator square root of u end fraction space fraction numerator d u over denominator 2 x minus 4 end fraction equals integral fraction numerator 2 over denominator square root of u end fraction d u equals 2 integral u to the power of negative 1 half end exponent d u equals 4 u to the power of negative 1 half end exponent plus C equals 4 square root of x squared minus 4 x plus 5 end root plus C$