Matematika

Pertanyaan

Tolong banget ya ka , 2 soal ini
Bnr butuh bantuan
Tolong banget ya ka , 2 soal ini Bnr butuh bantuan

1 Jawaban

  • $ (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.