5.4 Integration & Anti-derivatives

Indefinite Integrals

Question #1 (Easy): Finding the General Indefinite Integral

Strategy

The notation for the general indefinite integral is: . This represents the entire

anti-derivative family of .

So, always remember to add the constant term after the anti-derivative function .

Sample Question

Find the general indefinite integral.

Solution

1) This integral can be split into two integrals based on one of the properties of integrals:

So then,

2) Take the anti-derivate of each component:

and

3) Putting it together:

Though two constant factors are added, they represent an arbitrary number and so it can be

simply written as another .

Therefore, the general indefinite integral of

.

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###### Document Summary

Question #1 (easy): finding the general indefinite integral. The notation for the general indefinite integral is: ( ) ( ) . This represents the entire anti-derivative family of ( ). So, always remember to add the constant term after the anti-derivative function ( ). Solution: this integral can be split into two integrals based on one of the properties of integrals: So then, ( ) : take the anti-derivate of each component: And : putting it together: . Though two constant factors are added, they represent an arbitrary number and so it can be simply written as another .

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