Question

Integral. Tolong dijawab lengkap dengan caranya, thx

Answer 1

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∫ axⁿ dx = a/(n+1) x^(n+1) + c
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a) ∫ x³ dx= 1/4 x⁴ + c

b) ∫ dx/x⁴ = ∫ x⁻⁴ dx  = 1/(-3) x⁻³ + c = -¹/₃ x⁻³ +c =1 /(3x³) + c

c) ∫ ∫(2x² - 5x - 4) dx  = ²/₃ x³ - ⁵/₂ x² + 4x + c

d) ∫ (1-x)√x dx = ∫(1-x)x^(1/2) dx=  ∫x ^(1/2) - x^(3/2) dx
= ²/₃ x ³/² - ²/₅ x⁵/² + c
= ²/₃ x√x - ²/₅ x²√ x + c
= ²/₁₅ x√x ( 5 - 3x) + c

e) ∫ (x³ + 5x - 4) /(x²) dx = ∫ (x³ + 5x - 4)(x⁻²) dx
= ∫ x + 5x⁻¹ - 4x⁻² dx
= ¹/₂ x² + 5 ln x + 4 x⁻¹ + c
= ¹/₂ x² + 5 ln x + 4/x + c