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Integration

Question

Determine:

  1. ∫ 5x4 dx
  2. ∫ 3 dx
  3. ∫ 2 + x dx
Answer

  1. x5 + c
  2. 3x + c
  3. 2x + x2/2 + c
Note:

Integration is a reverse of derivative function.

∫ k dx = kx + c
∫ xn dx = xn+1/n+1 + c
∫ sin x dx = -cos x + c
∫ cos x dx = sin x + c

Multiplication by constant
∫ kxn dx = k ∫ xn dx

Sum Rule
∫ g(x) + h(x) dx = ∫ g(x) dx + ∫ h(x) dx

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