Matematika

Pertanyaan

Hasil dari :
1. ʃ x(x-2) (x+2) dx =
2. ʃ x²+x/x dx =
3. ʃ x²+2/√x dx =
4. ʃ (sec²x-tanx.secx) dx =
5. ʃ (2 cot²x-3 tan²x) dx =

2 Jawaban

  • ²Integral Tak Tentu

    1. ∫ x(x-2)(x+2) dx = ∫ x(x² -4) dx = ∫ x³ - 4x dx
    = ¹/₄ x⁴ - 2x² + c

    2. ∫ (x² +x) /(x) dx = ∫ x + 1 dx = ¹/₂ x² + x + c

    3. ∫ (x² + x)/(√x) dx= ∫(x² + x) (x⁻¹/²) dx = ∫( x³/² + x¹/²) dx
    = ²/₅ x⁵/² + ²/₃ x³/² +c
    = ²/₅ x² √x + ²/₃ x√x + c

    4.∫(sec² x - tan x sec x) dx  = ∫ sec² x dx - ∫ tan x sec x dx
    = tan x -  sec x + c

  • 2. 1/3 x^3 + x + c
    3. 1/3 x^3 + 2 . 2 x^1/2
    1/3 x^3 + 4 akar x

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