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Integration

Multiple, Sum and Difference Rules

The following rules also follow from the counterparts of differentiation:

1. Constant multiple rule

   m f(x) dx = m f(x) dx + c

2. Sum rule

   (f(x) + g(x)) dx = f(x) dx + g(x) dx + c

3. Difference rule

   (f(x) − g(x)) dx = f(x) dx − g(x) dx + c

Note that there are no general integration rules for products and quotients. There are rules for evaluating some special cases for them.

Examples

6cos θ dθ = 6sin θ + c

15x⁴ dx = 15(1/5)x⁵ + c = 3x⁵ + c

(y + 2)dy = ½y² + 2y + c

(e^2+y − 8y) dy = e²e^ydy − 8y dy = e^2+y − 4y² + c

Exercise

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

<< Basic Integrals | Integration Index | Linear Substitution >>