Pertanyaan

Hitung. 1 . ∫ 9 x 2 + 16 d x

Hitung.

$1$ . $\int \frac{d x}{9 x ^{2} + 16}$

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:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator d x over denominator 9 x squared plus 16 end fraction end cell equals cell integral fraction numerator d x over denominator 9 open parentheses x squared plus begin display style 16 over 9 end style close parentheses end fraction end cell row blank equals cell 1 over 9 integral fraction numerator 1 over denominator x squared plus begin display style 16 over 9 end style end fraction d x end cell end table$

Ingatlah bahwa:

$integral fraction numerator 1 over denominator x squared plus a squared end fraction d x equals 1 over a times arctan times x over a$

Kemudian diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over 9 integral fraction numerator 1 over denominator x squared plus begin display style 16 over 9 end style end fraction d x end cell equals cell 1 over 9 integral fraction numerator 1 over denominator x squared plus begin display style open parentheses 4 over 3 close parentheses squared end style end fraction d x end cell row blank equals cell 1 over 9 times fraction numerator 1 over denominator begin display style 4 over 3 end style end fraction times arctan times fraction numerator straight x over denominator begin display style 4 over 3 end style end fraction plus straight C end cell row blank equals cell 1 over 9 times 3 over 4 times arctan times straight x times 3 over 4 plus straight C end cell row blank equals cell 3 over 36 arctan fraction numerator 3 straight x over denominator 4 end fraction plus straight C end cell row blank equals cell fraction numerator arctan begin display style fraction numerator 3 straight x over denominator 4 end fraction end style over denominator 12 end fraction plus straight C end cell end table$

Maka, hasil integral dari $integral fraction numerator d x over denominator 9 x squared plus 16 end fraction$ adalah $fraction numerator arctan begin display style fraction numerator 3 x over denominator 4 end fraction end style over denominator 12 end fraction plus C$ .