Pertanyaan

Hasil dari ∫ ( x 2 + 6 x + 9 x + 3 ) 2 d x = …

Hasil dari $\int (\frac{x + 3}{x ^{2} + 6 x + 9})^{2} d x = \dots$

$fraction numerator 4 over denominator 3 left parenthesis x plus 3 right parenthesis to the power of 4 end fraction plus c$
$fraction numerator 4 over denominator 3 left parenthesis x plus 3 right parenthesis squared end fraction plus c$
$negative fraction numerator 1 over denominator 2 left parenthesis x plus 3 right parenthesis to the power of 4 end fraction plus c$

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

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Pembahasan

Diberikan bentuk integral seperti di atas. Dimisalkan : maka . Dengan demikian, hasil dari integral di atas adalah . Jadi, tidak ada jawaban yang tepat.

Diberikan bentuk integral seperti di atas. Dimisalkan : u equals x plus 3 maka d u equals d x .

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses fraction numerator square root of x plus 3 end root over denominator x squared plus 6 x plus 9 end fraction close parentheses squared space d x end cell equals cell integral open parentheses fraction numerator square root of x plus 3 end root over denominator left parenthesis x plus 3 right parenthesis squared end fraction close parentheses squared space d x end cell row blank equals cell integral open parentheses fraction numerator square root of u over denominator u squared end fraction close parentheses squared space d u end cell row blank equals cell integral u over u to the power of 4 space d u end cell row blank equals cell integral u to the power of negative 3 end exponent d u end cell row blank equals cell negative 1 half u to the power of negative 2 end exponent plus c end cell row blank equals cell negative fraction numerator 1 over denominator 2 left parenthesis x plus 3 right parenthesis squared end fraction plus c end cell end table$

Dengan demikian, hasil dari integral di atas adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 2 left parenthesis x plus 3 right parenthesis squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c end table$ .

Jadi, tidak ada jawaban yang tepat.