tolong jawab sama penyelesaiannya integral t^3+t / (t^4 + 2t^2 +1 )^4 dt tentukan hasil integral tersebut ....
Matematika
pumi
Pertanyaan
tolong jawab sama penyelesaiannya
integral t^3+t / (t^4 + 2t^2 +1 )^4 dt
tentukan hasil integral tersebut ....
integral t^3+t / (t^4 + 2t^2 +1 )^4 dt
tentukan hasil integral tersebut ....
2 Jawaban
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1. Jawaban Magriby
u = t^4 + 2t²+1
du/dt = 4t³+4t
dt = du/4t³+4t
integral t³+t / u^4 du/4t³+4t
= 1/4 integral u^-4 du
= 1/4 * 1/-3 u^-3 +C
= 1/-12 * (t^4+2t²+1)^-3 + C -
2. Jawaban whongaliem
∫(t³ + t) / (t^4 + 2t² + 1)^4 dt = ∫(t³ + t) (t^4 + 2t² + 1)^(- 4) dt
misal : u = t^4 + 2t² + 1
du/dt = 4t³ + 4t
= 4 (t³ + t)
dt = du / 4(t³ + t)
soal menjadi ....
∫(t³ + t) / (t^4 + 2t² + 1) = ∫(t³ + t) (t^4 + t² + 1)^(- 4) dt
= ∫(t³ + t) u^(- 4) du / 4(t³ + t) du
= ∫ (1/4) .u^(- 4) du
= - (1/12) u^ (- 3) + c
= - 1 / {12 u³ + c
= - 1 / {12 (t^4 + 2t² + 1)³ } + c