Matematika

Pertanyaan

Integral x pangkat 2 ln (x pangkat 2) dx adalah? Mohon bantuannya

2 Jawaban

  • integral x^2 dx
    = x^3 / 3 + C
    kalau ada yg ga paham tanya ya dek :)
  • Integral (x^2 ln (x^2)) dx
    = Integral (ln (x^2) . x^2) dx
    = Integral U dV
    U = ln (x^2)
    dU = 1/(x^2) . 2x dx => dU = 2/x dx

    dV = x^2 dx
    V = 1/3 x^3

    = Integral U dV
    = U . V - integral V dU
    = ln (x^2) . 1/3 x^3 - integral (1/3 x^3 . 2/x) dx
    = 1/3 x^3 ln (x^2) - integral (2/3 x^2) dx
    = 1/3 x^3 In (x^2) - 2/9 x^3 + C

    = 1/3 x^3 [ln (x^2) - 2/3] + C

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