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Unit 3: Integration by Parts

 Integration by parts is used when we observe two dissimilar functions that don’t appear to Notes
be associated to each other via a substitution.

 Whenever we utilize integration by parts, we make use of everything inside of the integral
for f and dg that comprises the dx.
 The magnificent substitution z = tan(x/2) permits alteration of any trigonometric integrand
into a rational one.

3.4 Keywords

Integration by Parts: It is a method depending on the product rule for differentiation, for
articulating one integral in provisions of another.

Substitution z=tan(x/2): The magnificent substitution z = tan(x/2) permits alteration of any
trigonometric integrand into a rational one.

3.5 Review Questions


1. Integrate x x  1 dx


2. Integrate x In x dx

3. Integrate x 2 In 4x dx
2

4. Integrate xe dx
2
5. Integrate x sec x dx

2 3x

6. Integrate x e dx
7. Integrate arcsin x dx


8. Integrate x cos3x dx

9. Integrate arcsin3x dx


10. Integrate 2 arctanx x dx

Answers Self Assessment

x

x
g
x
1. Integration by parts 2. f ( ). ( ) g ( ). ( )
f
x
3. diff. Coeft. of first integral of second 4. first
5. original 6. dissimilar
7. dx 8. products
9. False 10. True

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