Pertanyaan

Hitung. 2 . ∫ 4 x x 2 − 16 d x

Hitung.

$2$ . $\int \frac{d x}{4 x x ^{2} - 16}$

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Diperoleh intergalnya yaitu: Ingatlah bahwa: Kemudian diperoleh: Maka,hasil integral dari adalah .

Diperoleh intergalnya yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator d x over denominator 4 x square root of x squared minus 16 end root end fraction end cell equals cell 1 fourth integral fraction numerator 1 over denominator x square root of x squared minus 16 end root end fraction d x end cell row blank equals cell 1 fourth integral fraction numerator 1 over denominator x square root of x squared minus 4 squared end root end fraction d x end cell end table$

Ingatlah bahwa:

$integral fraction numerator 1 over denominator x square root of x squared minus a squared end root end fraction d x equals 1 over a times asec open parentheses fraction numerator open vertical bar x close vertical bar over denominator a end fraction close parentheses$

Kemudian diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 1 fourth integral fraction numerator 1 over denominator x square root of x squared minus 4 squared end root end fraction d x end cell equals cell 1 fourth times 1 fourth times asec open parentheses fraction numerator open vertical bar straight x close vertical bar over denominator 4 end fraction close parentheses plus straight C end cell row blank equals cell 1 over 16 times asec open parentheses fraction numerator open vertical bar straight x close vertical bar over denominator 4 end fraction close parentheses plus straight C end cell row blank equals cell fraction numerator asec open parentheses begin display style fraction numerator open vertical bar straight x close vertical bar over denominator 4 end fraction end style close parentheses over denominator 16 end fraction plus straight C end cell end table$

Maka, hasil integral dari $integral fraction numerator d x over denominator 4 x square root of x squared minus 16 end root end fraction$ adalah $fraction numerator asec open parentheses begin display style fraction numerator open vertical bar x close vertical bar over denominator 4 end fraction end style close parentheses over denominator 16 end fraction plus C$ .