Prog 15 Integration MEF

(1)

(2)

Functions of a linear function of _x Integrals of the form and

Integration of products – integration by parts Integration by partial fractions

Integration of trigonometric functions

( ) / ( )



(3)

Integration of products – integration by parts

Integration by partial fractions

( ) / ( )



(4)

Integration is the reverse process of differentiation. For example:

where C is called the constant of integration.

3 2 2 3

( ) 3 and 3



 

d

x x x dx x C

(5)

Standard integrals

What follows is a list of basic derivatives and associated basic integrals:

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Standard integrals

1 1

2 2

1 1

2 2

(cosh ) sinh sinh cosh

(sinh ) cosh cosh sinh

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(9)

( ) / ( )



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If:

then:

For example:

(11)

( ) / ( )



(12)

(a)

For example:

(13)

Integration of products – integration by parts Integration by partial fractions

( ) / ( )



(14)

The parts formula is:

For example:

(15)

( ) / ( )



(16)

If the integrand is an algebraic fraction that can be separated into its partial fractions then each individual partial fraction can be integrated separately.

For example:

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( ) / ( )



(18)

Many integrals with trigonometric integrands can be evaluated after applying trigonometric identities.

For example:

(19)

Integrate standard expressions using a table of standard forms

Integrate functions of a linear form

Evaluate integrals with integrands of the form and

Integrate by parts

Integrate by partial fractions

Integrate trigonometric functions

( ) / ( )

