Pertanyaan

Hasil dari ∫ tan 2 x sec 6 x d x = tan x a + b tan x + c tan 3 x .Nilai a + b - 3c = ….

Hasil dari $\int \frac{sec ^{6} x}{tan ^{2} x} d x = \frac{a}{tan x} + b tan x + c tan^{3} x$ . Nilai a + b - 3c = ….

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Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

nilai .

nilai

Pembahasan

Misalkan: u = tan ⁡x Maka, Sehingga, integral di atas menjadi, Diperoleh nilai Jadi, nilai .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses fraction numerator sec to the power of 6 invisible function application x over denominator tan squared invisible function application x end fraction close parentheses d x end cell equals cell integral open parentheses fraction numerator sec to the power of 4 invisible function application x over denominator tan squared invisible function application x end fraction times sec squared invisible function application x close parentheses d x end cell row blank equals cell integral open parentheses fraction numerator open parentheses sec squared invisible function application x close parentheses squared over denominator tan squared invisible function application x end fraction times sec squared invisible function application x close parentheses d x end cell row blank equals cell integral open parentheses fraction numerator open parentheses 1 plus tan squared invisible function application x close parentheses squared over denominator tan squared invisible function application x end fraction times sec squared invisible function application x close parentheses d x end cell end table end style$

Misalkan:
u = tan ⁡x

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d u over denominator d x end fraction end cell equals cell sec squared invisible function application x end cell row cell integral fraction numerator d u over denominator d x end fraction d x end cell equals cell integral sec squared invisible function application x d x end cell row cell integral d u end cell equals cell integral sec squared invisible function application x d x end cell end table end style$

Sehingga, integral di atas menjadi,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses fraction numerator open parentheses 1 plus tan squared invisible function application x close parentheses squared over denominator tan squared invisible function application x end fraction times sec squared invisible function application x close parentheses d x end cell equals cell integral open parentheses open parentheses 1 plus u squared close parentheses squared over u squared close parentheses d u end cell row blank equals cell integral open parentheses fraction numerator 1 plus 2 u squared plus u to the power of 4 over denominator u squared end fraction close parentheses d u end cell row blank equals cell integral open parentheses 1 over u squared plus 2 plus u squared close parentheses d u end cell row blank equals cell negative 1 over u plus 2 u plus 1 third u cubed end cell row blank equals cell negative fraction numerator 1 over denominator tan invisible function application x end fraction plus 2 tan invisible function application x plus 1 third tan cubed invisible function application x end cell end table end style$

Diperoleh nilai

Jadi, nilai .