## Integration Rules

### Integral of a Function

A function ๐(x) is called a primitive or an antiderivative of a function f(x), if**๐'(x) = f(x)**.

### Integration Rules

**Chain rule :**

**∫***u.v dx*=*uv*+ ……… + (–1)_{1}– u'v_{2}+ u''v_{3}– u'''v_{4}+ (–1)^{n–1}u^{n–1}v_{n}^{n}**∫**u^{n}.v_{n}dx

Where stands for*n*^{th}differential coefficient of*u*and stands for*n*^{th}integral of*v*.**Sum Rule**

**∫***(f + g) dx =***∫**f dx +**∫**g dx**Difference Rule**

**∫**(f - g) dx =**∫**f dx -**∫**g dx**Multiplication by constant**

**∫**cf(x) dx = c**∫**f(x) dx**Power Rule (n≠-1)**

**∫**x^{n}dx = x^{n+1}/(n+1) + C

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