Pertanyaan

∫ ( 3 x 4 − 2 x 2 + 1 ) 3 x ( 3 x 2 − 1 ) d x = ....

$\int \frac{x ( 3 x ^{2} - 1 )}{( 3 x ^{4} - 2 x ^{2} + 1 ) ^{3}} d x = ....$

$fraction numerator negative 2 over denominator square root of 3 x to the power of 4 minus 2 x squared plus 1 end root end fraction plus C$
$fraction numerator negative 2 over denominator 3 square root of 3 x to the power of 4 minus 2 x squared plus 1 end root end fraction plus C$
$fraction numerator negative 1 over denominator 2 square root of 3 x to the power of 4 minus 2 x squared plus 1 end root end fraction plus C$

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Habis dalam

Klaim

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Dengan menggunakan integral substitusi diperoleh: Sehingga

Dengan menggunakan integral substitusi diperoleh:

$u equals 3 x to the power of 4 minus 2 x squared plus 1 fraction numerator d u over denominator d x end fraction equals 12 x cubed minus 4 x d x equals fraction numerator d u over denominator 4 x left parenthesis 3 x squared minus 1 right parenthesis end fraction$

Sehingga

$integral fraction numerator x left parenthesis 3 x squared minus 1 right parenthesis over denominator square root of open parentheses 3 x to the power of 4 minus 2 x squared plus 1 close parentheses cubed end root end fraction space d x equals integral fraction numerator begin display style up diagonal strike x up diagonal strike left parenthesis 3 x squared minus 1 right parenthesis end strike end style over denominator begin display style square root of u space cubed end root end style end fraction space fraction numerator begin display style d u end style over denominator 4 up diagonal strike x up diagonal strike left parenthesis 3 x squared minus 1 right parenthesis end strike end fraction equals integral 1 fourth u to the power of negative 3 over 2 space end exponent d u equals fraction numerator 1 over denominator up diagonal strike 4 end fraction. open parentheses negative up diagonal strike 2 close parentheses space u to the power of negative 1 half end exponent plus C equals negative fraction numerator 1 over denominator 2 square root of u end fraction plus C equals negative fraction numerator begin display style 1 end style over denominator begin display style 2 square root of 3 x to the power of 4 minus 2 x squared plus 1 end root end style end fraction plus C$