Matematika

Pertanyaan

integral subtitusi dari∫ x (x+4)5 dx = ....
a. 1/21 (3x+26)(x+4)^6 +C
b. 1/21 (3x- 14)(x+4)^6 +C
c. 1/21 (3x-10)(x+4)^6 +C
d. 1/21 (3x+2)(x+4)^6 +C
e. 1/21 (3x-2)(x+4)^6 +C

1 Jawaban

  • jawab

    ∫ x (x + 4)⁵ dx

    substitusi
    u  = x+ 4 → x = u - 4
    du = dx

    ∫ x (x + 4)⁵ dx = ∫ (u-4)(u)⁵ du
    = ∫ u⁶ - 4u⁵ du
    = 1/7 u⁷ - 4/6 u⁶ + c
    = 1/7 (x+4)⁷ - 2/3 (x+4)⁶ + c
    = 1/21 (x+4)⁶ { 3(x+4) - 14} + c
    = 1/21 (x+4)⁶  (3x +12 - 14) + c
    = 1/21 (3x -2 )(x+4)⁶ + c


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