![](Image336.gif)
Some Rules for Integration
![](Image337.gif)
![](Image338.gif)
Example 1
Evaluate ![](image339.gif)
Solution : Using rule 2, we find that
![](Image340.gif)
![](imgsol1.gif)
Also, using formula ( 1 ), we get
![](imgsol2.gif)
![](imgsol3.gif)
Example 2
Evaluate ![](image341.gif)
Solution : Using rule 2 and formula (4), we get
![](imgex2sol1.gif)
Example 3
Evaluate ![](image342.gif)
Solution : ![](imgex3sol1.gif)
Example 4
Evaluate ![](image343.gif)
Solution : ![](imgex4sol1.gif)
using rules 1, 2 and applying standard results (1), (2), we get
![](imgex4sol2.gif)
Example 5
Evaluate
Solution : ![](imgex5sol1.gif)
using (22), with a2 = 49, we get
![](imgex5sol2.gif)
Example 6
![](imgex6.gif)
Solution : ![](imgex6sol1.gif)
applying (24), we get
![](imgex6sol2.gif)
Example 7
Evaluate
![](imgex7.gif)
Solution :
![](imgex7sol1.gif)
By rule (1) and (2), we have
![](imgex7sol2.gif)
Using standard results (1), (4), (13) and (11) respectively, you find
![](imgex7sol3.gif)
Example 9
Integrate w. r. to x. the following
![](imgex9.gif)
Solution :
![](imgex9sol1.gif)
Using (1), (3), (4), (5) and again (1) respectively we get
![](imgex9sol2.gif)
Example 10
Integrate w. r. to. x, the following
![](imgex10.gif)
Solution :
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