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Integration

Basic Integrals

By using the basic formulas of derivatives we can verify the following:

  1. the indefinite integral ofm dx = mx + c, for any number m.
  2. the indefinite integral ofxn dx =1 over (n plus 1) times x to the power of (n plus 1) + c, if n ≠ 1.
  3. the indefinite integral of1 over xdx = ln |x| + c, for x ≠ 0.
  4. the indefinite integral of sin x dx = −cos x + c
  5. the indefinite integral of cos x dx = sin x + c
  6. the indefinite integral of ex dx = ex + c

Note that the variable x used above can be replaced by any other symbol.

Examples

the indefinite integral of cos θ dθ = sin θ + c

the indefinite integral of15 dx = 15x + c

the indefinite integral ofy dy = ½y2 + c

the indefinite integral of 1 over x squared is negative 1 over x

Exercise

Do plenty of exercises until you feel confident of these basic integrals.

Find the indefinite integrals:

indefinite integral =

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