Tolong banget ya ka , 2 soal ini Bnr butuh bantuan
Matematika
drezygio12
Pertanyaan
Tolong banget ya ka , 2 soal ini
Bnr butuh bantuan
Bnr butuh bantuan
1 Jawaban
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1. Jawaban dharmawan14
$ (2-4x)/(x^2-x-3)^3 dx
misal u = x^2 -x -3
du/dx = 2x-1
dx = du/(2x-1)
$ (2-4x) u^-3 du/(2x-1)
= $ -2(-1+2x) u^-3 du/(2x-1)
= -2 $ u^-3 du
= -2.(u^-2)/-2 + c
= u^-2 + c
= 1/u^2 + c
= 1/(x^2-x-3)^2 + c ==> B
27) $ x (x+1)^1/2 dx
misal u = x +1. => x = u-1
du/dx = 1
dx = du
$ (u-1).u^1/2 du
= $ (u^3/2 - u^1/2) du
= (u^5/2)/(5/2) - (u^3/2)/(3/2) + c
= 2/5(u^5/2) - 2/3(u^3/2) + c
= 6/15(u^5/2) - 10/15(u^3/2) + c
= 6/15(u^3/2)(u) - 10/15(u^3/2) + c
= u^3/2 (6/15u - 10/15) + c
= (x+1)^3/2 { 6/15(x+1) - 10/15 } +c
= (x+1)^3/2 {6/15x - 4/10 } + c
= (x+1)^3/2 {6/15x - 4/15 } + c
= 2/15(x+1)^3/2(3x -2)+c
jadi jawabannya E.