Pertanyaan

Hasil dari ∫ 2 x 2 − 6 x + 5 ( 2 x − 3 ) d x = ...

Hasil dari $\int \frac{( 2 x - 3 ) d x}{2 x ^{2} - 6 x + 5} = ...$

$fraction numerator 1 over denominator square root of 2 x squared minus 6 x plus 5 end root end fraction plus C$

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

$M i s a l colon space u equals 2 x squared minus 6 x plus 5 d u equals 4 x minus 6 space d x d u equals 2 left parenthesis 2 x minus 3 right parenthesis d x d x equals fraction numerator d u over denominator 2 left parenthesis 2 x minus 3 right parenthesis end fraction integral fraction numerator left parenthesis 2 x minus 3 right parenthesis d x over denominator square root of 2 x squared minus 6 x plus 5 end root end fraction equals integral fraction numerator begin display style fraction numerator 2 x minus 3 right parenthesis d u over denominator 2 left parenthesis 2 x minus 3 right parenthesis end fraction end style over denominator u to the power of begin display style 1 half end style end exponent end fraction equals 1 half integral fraction numerator d u over denominator u to the power of begin display style 1 half end style end exponent end fraction equals 1 half integral u to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent d u equals 1 half. fraction numerator 1 over denominator begin display style 1 half end style end fraction u to the power of 1 half end exponent equals 1 half.2. u to the power of 1 half end exponent equals u to the power of 1 half end exponent equals square root of 2 x squared minus 6 x plus 5 end root plus C$